Associate Professor
Sabanci University, Faculty of Engineering and Natural Sciences
I am an Associate Professor in the Mechatronics Engineering Program at Sabanci University. I earned my B.S and M.S. degrees in Mechanical Engineering at Middle East Technical University, Ankara, Turkey in 2006 and 2009, respectively, before joining at Carnegie Mellon University (CMU) in Pittsburgh, USA. At CMU, I worked in the Multi-scale Manufacturing and Dynamics Laboratory to understand the dynamic behaviour of the mechanical micromachining process. After I graduated in 2014, I continued working in the same laboratory as a postdoctoral research associate until August 2015.
My research interests focus on developing novel high-fidelity dynamic modeling approaches to accurately and precisely capture the vibrational behavior of complex engineering structures, experimental modal analysis techniques, advancing multi-scale manufacturing processes and related equipment/sensors, and fabrication of micro-scale bio-devices.
Sabanci University, Faculty of Engineering and Natural Sciences
Sabanci University, Faculty of Engineering and Natural Sciences
Middle East Technical University, Faculty of Engineering
Carnegie Mellon University, College of Engineering
Ph.D. in Mechanical Engineering
Carnegie Mellon University, College of Engineering
Master of Science in Mechanical Engineering
Middle East Technical University, Faculty of Engineering
Bachelor of Science in Mechanical Engineering
Middle East Technical University, Faculty of Engineering
Structural Dynamics Research Group is located in the Faculty of Engineering and Natural Sciences at Sabanci University and led by Dr. Bekir Bediz. Our primary research interests include (1) developing high fidelity and computationally efficient models to accurately predict the dynamics of multi-dimensional complex structures of multi-physics nature, (2) applying these developed techniques in emerging high-impact engineering problems, (3) modal testing and analysis, (4) modeling and experimentation of manufacturing processes, specializing in mechanical manufacturing and its applications.
Stiffened laminated panels are widely used in the aviation (aerospace), marine, and automotive industries due to their high stiffness-to-weight ratio. Stacking sequence, stiffener size, type, and location have significant effects on the mechanical performance of these structures. To achieve a lightweight structural design and meet the requirements of engineering applications, the concurrent layout and stacking sequence optimization of stiffened laminated composite panels poses a challenging problem due to the large number of design variables. Therefore, it is critical to develop a novel high-fidelity numerical solution and design methodology.
In literature, the conventional prevailing analysis approach is finite element method. This method requires an alternative, discrete representation of the structure/geometry. Although the analysis process starts with the CAD model, it is necessary to convert this CAD model into a suitable finite element mesh for analysis. This mesh structure is obtained by dividing the geometry into many simple geometric shapes with straight edges to accurately express a structure having a complex geometry. Therefore, as the number of elements are increasing, the computational burden of the finite element approach increases as well.
In this project, to overcome this problem, the overarching goal is to develop a new high-fidelity spectral element solution methodology and to develop a novel coarse quad mesh generation methodology, that is based on NURBS enabling accurate representation of the geometry, capable of incorporating curved edges for the elements and suitable with the proposed solution approach. Since high order polynomials can be used in the elements with this spectral element approach, geometry can be taken into account correctly and the analysis can be performed with high precision. However, although more degrees of freedom are defined within the element, the total degrees of freedom will be less compared to the finite element method, since the structure will be divided into much fewer elements. This will lead to faster simulation duration in the design process which is the main advantage of the proposed solution methodology.
The application of micro-milling for the fabrication of micro-scale parts/features from a plethora of materials has found significantly increased usage. In this fabrication process, miniaturization of mechanical components requires smaller machine tools with ultra-high rotational speeds. However, such rotational speeds complicate the spindle's dynamic response and affect the machining process's quality. Although contact or air bearings are generally used in micro-milling spindles, active magnetic bearing is a promising technology because it enables high-speed and contact-free rotation with active control of the spindle dynamics. Active magnetic bearings are being extensively studied to provide the benefits of regulated magnetic levitation and ultra-high speeds to the machining industry with condition monitoring and disturbance rejection capabilities such as chatter suppression. The primary objective of this project is to design and optimize active magnetic bearing spindles for micro-milling applications and demonstrate a multiobjective optimization scheme that can be adapted to different application requirements.
Due to their high stiffness-to-weight ratio, laminated composite structures are widely used in many fields of engineering such as aviation, automotive and ship industry. Most of the time, these laminated composite panels are exposed to dynamic forces that can cause resonances; thereby leading to excessive vibrations or even failures/malfunctions. Since these structures can be tailored in the design process, achieving an optimum design in these structures will prevent any adverse effect during its operation.
Until recently, constant stiffness laminated composites were mostly used in these structures, where each layer of the composite structure (each laminate) was produced using a certain fiber angle. The desired design strength and dynamic properties of these flat fibers in each layer can be optimized to increase the required performance of the part. With the recent technological advancements in manufacturing of composite materials, laminates with variable stiffness properties can be produced using curvilinear fibers within each layer. Since these laminates provide better load distribution within the structure, they can perform better both statically and dynamically compared to constant stiffness composite structures.
The main goal of this study is to design the curvilinear fiber paths of variable stiffness laminated composite structures to meet the design requirements using multi-objective optimization approaches and a high-fidelity modeling technique to accurately and (computationally) efficiently predict the dynamics of variable stiffness laminated composite structures.
The biggest problem encountered in transdermal drug applications is the limitation in the passage of the active substance (active molecules) through the epidermis barrier. Unless physical or chemical penetration is increased, the stratum corneum (SC) does not allow the passage of molecules larger than 500 Da. Strategies such as sonophoresis, fractional photothermolysis, thermophoresis, iontophoresis, magnetophoresis, and electroporation have been developed to overcome this, but these methods have not become widespread due to the cost and complexity associated with their application in the clinical setting. This situation imposes significant limitations on transdermal treatments and prevents the transdermal application of many bioactive agents. In addition, skin irritation side effects are a very common problem in topical applications of this type. It is recognized that intradermal drug delivery methods can overcome many difficulties/problems in topical applications. Intradermal dosing allows for more effective administration of small molecules, biologics, and agents such as vaccines with improved bioavailability. However, the technical difficulties in performing intradermal injections (hypodermic injector) today, which require special training and have low reproducibility, have led to the limitation of this drug delivery method. Therefore, due to several advantages, microneedle arrays are a promising drug delivery system. Conventional methods in the treatment of OA of this method bring many negative consequences, especially side effects in the gastrointestinal tract. Therefore, GAG, CS and HA used in the treatment should be administered alone or together, in much lower doses, with an approach that will provide a long effect and keep the plasma level constant. The use of intradermal microneedle arrays may be advantageous in reducing or instantly eliminating possible side effects and toxicity.
Vibration behavior of composite structures is critical for a broad range of applications in diverse industries such as aerospace, automotive, and ship-building. This concept has attracted increasing attention due to its flexibility to achieve desired material properties (such as to obtain high specific strength and high specific rigidity) and its wide range of applications. A large body of literature has been devoted to the modeling dynamics (vibrational behavior) of composite structures. However, most of the studies focus on simple geometries and boundary conditions such as beam (one-dimensional) and rectangular or circular plate (two-dimensional) models. And the methods developed using higher order modeling approaches are generally computationally inefficient. In this study, our aim is to develop a novel modeling approach that will enable accurately and (computationally) efficiently capturing the dynamics of different kinds of composite stuctures having arbitrary geometries and boundary conditions.
Piezoelectric structures have been widely used in a range of applications including vibration control, energy harvesting, structural health monitoring, and also surface haptics over the past few decades. Among the transducers that convert the mechanical (electrical) energy to electrical (mechanical) energy, piezoelectric transducers are mostly preferred to the electromagnetic and electrostatic ones due to their high power density and ease of manufacturing at different size scales. The most common use of piezoelectric materials in the form of patches/layers is by integrating them to the surfaces of flexible beam/plate-like structures, and thus utilizing the bending motion for generating electrical signal and vice versa (applying a voltage to generate a bending deformation).
In this project, we are developing a novel multiphysics modeling approach based on spectral-Tchebychev technique to maximize the electricity generation via energy harvesting.
In this project, it is aimed to design and develop a new automated impact excitation system for repeatable, high-bandwidth, controlled-force modal testing of structures. In the foreseen system, a force sensor (load cell) with a capacity to make precise force measurements at high bandwidth will be connected to a tailor made flexible flexure-based connection piece. The impacts will be provided automatically by prescribing an initial deflection to the flexible connection piece; once the system is released, it will start to move towards the test structure. To automate the system, both the impact excitation system and the tested structure will be modeled and a closed-loop feedback system will be created. To validate the developed models and evaluate the performance of the impact excitation system, a set of experiments will be conducted.
It is highly challenging to predict the dynamics of (assembled) structures that are too large or complex to be analyzed as a whole. To address this issue, I will develop an ST simulation framework to analyze highly complex structures. To predict the dynamics of (assembled) structures, a substructuring algorithm will be applied to divide the complex structure into simpler geometries. Then, each of these simpler substructures will be solved using the ST method. Depending on the geometry of each substructure and also to increase the numerical efficiency, either a 1D-, 2D-, or 3D-ST approach (1D- and 3D-ST approaches are already developed during my graduate studies) will be implemented to obtain dynamic behavior. Lastly, to obtain the overall dynamics of the assembly structure, substructures will be combined via a component mode synthesis approach or a frequency based coupling technique.
The first application of this study will be on predicting the workpiece dynamics. During the machining operation, the dynamic behavior of the workpiece changes continuously due to mass removal. The interaction between the workpiece and the cutting tool affects the process quality. Since the dynamics of the workpiece changes during cutting, its effect should be taken into account to accurately determine the process stability.
Mechanical micromachining is an emerging technique for producing three-dimensional complex micro-scale geometries on a broad range of materials. In particular, it finds applications in biomedical and analytical devices, tribological surfaces, and medical devices. Effectively addressing the strict accuracy requirements of the micromachining application necessitates understanding and control of dynamic behavior of micromachining system, including motion actuators, spindle, and the tool, as well as their coupling with the mechanics of the material removal process. The dynamic behavior of the tool-holder-spindle-machine assembly, as reflected at cutting tip of a micro-tool, often determines the achievable process efficiency and quality. However, the existing (macro-scale) technique cannot be used to accurately model micromachining dynamics. Furthermore, new experimental techniques are needed to determine the speed-dependent modal characteristics of the ultra-high-speed spindles that are used during micromachining. The overarching objective of this research project is to derive and validate models for the micromachining process dynamics to enable prediction of micromachining process accuracy and efficiency (throughput).
Laminated panels are widely used in various industries due to their distinct advantages. The design of laminated composites requires efficient methodologies due to the vast design space. This study proposes a new spectral element modeling approach for accurate and computationally efficient analysis of laminated composites with arbitrarily shaped cutouts. The method employs a coarse quad meshing approach and a spectral Chebyshev method to determine the element matrices. The presented method enables obtaining high-fidelity models by applying - and -refinements following a non-dimensional approach, aiming to yield a model with the fewest degrees of freedom to achieve a desired convergence level. Benefiting from the advantages of both meshless methods (in terms of computational efficiency) and finite element methods (in terms of geometric capabilities), we performed several case studies for laminated panels with cutouts and it is shown that the presented spectral element method (SEM) enables calculating the natural frequencies and the mode shapes as accurate as FEM, yet decreases the analysis duration by 13 folds. Furthermore, the developed approach was employed with a gradient-based optimizer or genetic algorithm to demonstrate the design of (sandwich) laminated composites for obtaining optimal lamination parameters and 2D Pareto fronts.
Particle dampers (PD), a passive damping technology, absorb energy from particle-particle and particle-cell wall interactions originating from friction and collision. PDs offer advantages such as design simplicity, low cost, applicability in harsh conditions, and flexibility to be used in a wide frequency band range. Additive manufacturing, specifically the powder bed fusion process, can fabricate structures with integrated PDs in a single printing process, eliminating the need to implement external dampers. However, the dynamic behavior of PDs must be determined to utilize their full potential. In this study, we examined 16 cases of integrated PDs by varying specific parameters including size, number, and locations on the structure to understand the effects of these parameters on the dynamic behavior of the first and second modes of the structure. Modal tests were conducted on additively manufactured samples to extract frequency response functions and calculate modal parameters (natural frequency and damping ratio) using the rational fraction polynomial method, studying the effects of PDs. The results showed that the damping performance of the parts was increased by a factor of up to 10 using body-integrated PDs compared with the fully fused specimen. The effectiveness of body-integrated PDs was shown to be strongly dependent on their volume and location. For instance, the damping generally increased as the volume fraction increased, which also reduced the total weight of the specimens by up to 60 g. Furthermore, the damping performance significantly increased for a specific mode when the PDs were located near the maximum displacement regions.
The in-plane fiber orientations of variable stiffness (VS) laminates can be tailored to achieve enhanced structural properties compared to conventional constant stiffness (CS) laminates. However, VS laminate manufacturing faces challenges such as wrinkles, gaps, and overlaps. To address these challenges, we present a novel three-step design methodology. First, the laminate is modeled using lamination parameters (LPs) and the spectral Chebyshev method, and the optimal LPs are determined to maximize the fundamental frequency. Then, the discrete fiber angles are retrieved using the optimal LP distribution. Lastly, a normalized-cut segmentation method is applied to divide the domain into clusters and to generate manufacturable curvilinear fiber paths. Case studies focusing on designing clusters containing both straight and curvilinear fiber paths demonstrate that the designed VS composites can significantly enhance the dynamic performance with up to 20% enhancement in the fundamental frequency compared to CS laminates, under fully clamped boundary conditions with manufacturing constraints.
Stiffened composite panels are increasingly used in aerospace, marine, and automotive industries due to their lightweight and high-strength properties. However, determining the optimal stacking sequence and/or layout of stiffeners concurrently while adhering to manufacturing guidelines and empirical rules is challenging. To address this issue, we propose a novel one-step optimization framework that couples a highly accurate and computationally efficient spectral element modeling technique with an index-based optimization approach that inherently satisfies the manufacturing guideline and empirical rules. Spectral element modeling (SEM) combines the high accuracy of spectral (meshless) methods with the geometric flexibility of finite element methods. To determine the optimal design, an index-based optimization is proposed to decrease the number of design variables and remove the constraints. We demonstrated the accuracy and computational performance of SEM with results obtained by finite element analysis on composite laminates with and without a cutout. Finally, we applied the proposed optimization framework to various stiffened composite (balanced and symmetric) laminates of up to 200 plies to demonstrate its capability and efficiency.
The design of variable stiffness laminates requires efficient methodologies due to the increased number of optimization variables associated with curvilinear fiber paths. Here, this need is addressed by the development of two novel approaches: the lamination parameter extrapolation method (LPEM) and the relaxed lamination parameter interpolation method (RLPIM). These techniques build on the previously proposed lamination parameter interpolation method (LPIM), and collectively they form a spectrum of approaches that differ in optimization capacity, conservativeness regarding fiber curvature constraints, and computational cost. The resulting governing equations are solved using the spectral Chebyshev method to further improve the efficiency of the optimization process. The case studies demonstrate the effectiveness and unique properties of the developed algorithms.
This paper investigates the effect of stacking sequence on the power output of a smart composite panel integrated with piezoelectric patches, using lamination parameter formulation and spectral element method (SEM). The deformation of the panel is expressed using the first-order shear deformation theory. The strain energy of the host plate is formulated using lamination parameters and the governing equations are derived following Hamilton’s principle. To solve the governing equations accurately and efficiently, a spectral element method is applied where the structure is divided into regions that are continuous in terms of geometry, and element matrices of each region are calculated using the spectral Chebyshev approach. This method benefits both from the (geometry) flexibility of the finite element method and the accuracy of the meshless methods. The developed electromechanical model is used to study the effect of the number of piezo patches and their sizes. To demonstrate the accuracy and performance of the presented SEM, six case studies were investigated by comparing natural frequencies, structural/voltage frequency response functions (FRFs), and computational duration to those obtained from a finite element analysis (FEA). The maximum difference in the predicted natural frequencies between the SEM and FEA results is below 1% and the FRFs obtained using the presented solution technique excellently match the FEA results. Yet, the simulation duration is significantly reduced compared to FEA. To exploit the computational efficiency of the presented analysis approach, optimization case studies were also performed implementing a genetic algorithm to maximize the power output by optimizing the stacking sequence and patch distribution.
This study presents the spectral Chebyshev technique (SCT) for nonlinear vibrations of rotating beams based on a weak formulation. In addition to providing a fast-converging and precise solution for linear vibrations of structures with complex geometry, material, and physics, this method is further advanced to be able to analyze the nonlinear vibration behavior of continuous systems. Rotational motion and material gradation further complicate this nonlinear behavior. Accordingly, the beam is considered to be axially functionally graded (FG) and a model representing the forced nonlinear vibrations of the beam about steady-state equilibrium deformations (SSEDs) is developed. The model includes Coriolis, centrifugal softening, and nonlinear stiffening effects caused by coupling of the axial, chordwise, and flapwise motions, and large amplitude deformations. The integral boundary value problem for the rotating structure is discretized using the SCT and element-wise multiplication definition. As a result, mass, damping, and stiffness matrices, as well as internal nonlinear forcing functions and external forcing vectors, are obtained for a given rotating beam. This formulation provides a general representation of nonlinear strain relations in matrix form and circumvents the complexity rising from obtaining and solving the partial differential equations directly. In addition, nonlinear forcing functions are obtained in matrix form which facilitates the application of harmonic balance method easier to obtain the forced nonlinear response.
This study presents a meshless modeling approach to design variable-stiffness laminates considering manufacturing constraints. The governing equations are derived using lamination parameters and first-order shear deformation theory. The solution approach uses Chebyshev polynomials and Galerkin’s method to obtain the discretized equations of motion. The developed framework was used to maximize the fundamental frequency of composite plates. The variable-stiffness designs provided up to 28.4% higher frequencies compared to optimum constant-stiffness laminates, although the actual level of improvement depends on the number of layers. Finally, manufacturable fiber paths were obtained considering the allowed fiber curvature, which can also reduce the frequency values.
In this study, static and vibration behavior of a curved thick sandwich-structured composite composed of a honeycomb core layer and two face-sheets reinforced with carbon nanotubes is investigated. The governing equations are derived using three-dimensional elasticity equations and Hamilton’s principle. The problem domain is discretized following Gauss–Lobatto sampling approach. To numerically solve the governing equations, a spectral method based on Chebyshev polynomials is used and a CPU–GPU based hybrid solver is developed. The presented approach is validated by comparing the predicted natural frequencies and deformation of the structure to those obtained from finite element analysis. The results show that in-house CPU–GPU based spectral solution approach decreases the computational duration remarkably and predicts the dynamic and static behavior of the system accurately. Since composite materials offer great flexibility in tailoring the dynamic behavior of the structure, an optimization study is also performed to benefit from the developed computationally efficient solver. In this study, the CNT orientations are selected as design variables to maximize the fundamental frequency of the structure. Based on the analyzed cases for different thickness ratios, curvature amounts, volume content, and distributions of CNTs, it is shown that the vibration behavior of the structure can be significantly tailored.
Mechanical micromachining has become a leading approach to fabricate complex three-dimensional microscale features and miniature devices on a broad range of materials. To satisfy the accuracy and productivity demands of various micromachining applications, the tool-tip dynamics, i.e., the dynamic behavior of the tool-ultra high-speed spindle assembly as reflected at the cutting edges of a micro-tool, should be well-understood. However, existing techniques for predicting tool-tip dynamics pose strict limitations in frequency bandwidth and do not capture the effect of the spindle speed on tool-tip dynamics. In addition, those techniques cannot be applied broadly to predict tool tip dynamics for a myriad of microtool geometries. This paper presents a systematic approach to predicting the tool-tip dynamics accurately in micromachining when using ultra-high-speed (UHS) spindles and for arbitrary microtool geometries. The speed-dependent dynamics of UHS spindle are obtained using an experimental approach. The dynamics of micro tools are obtained analytically using the spectral Tchebychev technique, such that any microtool geometry can be modeled accurately and does not require new testing. The tool-tip dynamics are then predicted by combining (coupling) the spindle and micro tool dynamics using a novel modal-Tchebychev domain coupling technique. This technique enabled accurate coupling/decoupling of substructure dynamics within a broad frequency bandwidth (up to 15 kHz) and at different spindle speeds (up to 120,000 rpm). Furthermore, an empirical model for the mode-splitting effect is derived to capture the effect of spindle speeds on tool-tip dynamics. The overall approach is demonstrated and experimentally validated on an UHS spindle with microtool blanks and micro endmills at operational speeds. We conclude that the presented methodology can be used to determine the tool-tip dynamics accurately.
The steady-state equilibrium deformations (SSEDs) caused by centrifugal force field in rotating blades are not necessarily perturbed disturbances. These deformations can be considered as large amplitude deformations, especially for high values of the rotating speed. Accordingly, in the current study, geometrically nonlinear terms are included in the static analysis under centrifugal forces (SACF) to accurately model the stiffening/softening effects in the vibrations of rotating pre-twisted blades. To this end, by developing a shell model based on first-order shear deformation theory (FSDT), nonlinear and linear integral boundary value problems (IBVPs) governing the SSEDs and vibrations of the blade are obtained, respectively. Multi-mode discretization of these IBVPs is carried out by the spectral Chebyshev technique. The discretization of the nonlinear IBVP results in nonlinear algebraic equations. By solving these equations, nonlinear pre-stressed analysis (NPA) is performed to achieve the SACF. Then, the free vibrations of the rotating pre-twisted blade about the determined equilibrium position is investigated. The numerical results show that the natural frequencies obtained in the presence of the nonlinear terms are extremely lower than those of the linear pre-stressed analysis.
Deniz araçlarında kullanılan deniz ekipmanlarında istiflenmiş verimliliği artırmak adına çok fonksiyonlu sistemler önem kazanmaktadır. Yatlarda personelin iskele ile irtibatını sağlayan hareketli köprü sistemleri olarak geçit merdivenleri, denize iniş merdiveni olarak kullanılan yüzme merdivenleri ve küçük deniz araçlarının güverteden denize transferini sağlayan vinçler bulunmaktadır. Bu çalışmada çok fonksiyonlu paralel geçit merdiveni tasarımı, kinematik ve dinamik analizleri yapılmıştır. Geliştirilen paralel mekanizma sayesinde geleneksel geçit merdivenlerine fonksiyonellik eklenerek hem denize inişi sağlayan yüzme merdiveni ve platformu olarak kullanılması hem de teknede bulunan deniz motoru gibi deniz araçlarının denize indirilmesi ve iskeledeki yüklerin tekneye transferi adına bir tür vinç olarak kullanılması sağlanmıştır. Sistemin ilk tasarımı çubuk mekanizmaları ile oluşturularak gerçekleştirilmiştir. Gerekli tasarım parametreleri kinematik analiz sonucu elde edilmiştir. Analiz çıktılarına göre mekanizmanın üç boyutlu (3B) modellemesi SolidWorks bilgisayar destekli tasarım (CAD) programı kullanılarak oluşturulmuştur. Modelin yük altındaki davranışını incelmek adına dinamik analizi sonlu elemanlar yöntemi kullanılarak sağlanmıştır. Çoklu gövdelerden oluşan modellerde sistem hareketini sağlayan eyleyicilerdeki torku hassas bir şekilde hesaplamak için ANSYS programı kullanılmış ve analitik yolla elde edilen kinematik analiz sonuçları doğrulanmıştır. Tekne tasarım isterilerine ve ilgili güvenlik kurallarına (BUREAU VERITAS-NI629-DTR00E) göre nihai tasarımı yapılan geçit merdiveninin prototipi üretilmiştir.
Composite materials are widely used in various industries because of their distinct properties. Hybridization is an efficient way of designing composite panels to decrease the cost and/or weight while maintaining stiffness properties. In this study, an accurate and efficient framework is developed to optimize laminated sandwich panels composed of high-stiffness face sheets and low-stiffness core. The stiffness properties of face sheets and core are represented using lamination parameters. The governing equations are derived following first-order shear deformation theory and solved using the spectral Chebyshev approach. In multi-objective optimization problems, genetic algorithm is used to determine Pareto-optimal solutions for fundamental frequency, frequency gap, buckling load, and cost metrics. In these analyses, optimal lamination parameters and thickness are found for face-sheets and core of sandwich panels, and the results are presented as 2D and 3D Pareto-optimal design points. When the individual performance metrics lead to different optimum points, a scattering behavior is observed in the 3D Pareto sets whose boundaries are defined by the 2-objective Pareto fronts. The results provide insights into the design requirements for improving the dynamic and load-carrying behavior of sandwich laminates while minimizing the cost that presents the usability of the presented approach in the multi-objective optimization.
This study presents a modeling approach to accurately and efficiently predict the dynamics of laminated conical shells. The governing equations are derived based on the first order shear deformation theory kinematic equations following the Hamilton’s principle. To express the strain energy of the shells, in-plane and bending lamination parameters are used. A two-dimensional spectral approach based on Chebyshev polynomials is implemented to solve the governing equations. The developed framework including the spectral-Chebyshev approach and lamination parameters results in an accurate and computationally efficient solution method. To demonstrate the performance of the presented solution approach, various case studies including straight panels, curved shells, and truncated conical shells are investigated. The benchmarks indicate that the calculated non-dimensional natural frequencies excellently match the results found using finite element method and the simulation duration can be decreased by 100 folds. To leverage the computational performance of the presented approach, a stacking sequence optimization is performed to maximize the fundamental frequency of a shell geometry, and the corresponding fiber angles are retrieved from the optimized lamination parameters. Furthermore, a parametric analysis is performed to investigate the effect of geometry on the optimized lamination parameters (and fiber angles) based on fundamental natural frequency maximization.
The purpose of the current study was to develop an accurate model to investigate the nonlinear resonances in an axially functionally graded beam rotating with time-dependent speed. To this end, two important features including stiffening and Coriolis effects are modeled based on nonlinear strain relations. Equations governing the axial, chordwise, and flapwise deformations about the determined steady-state equilibrium position are obtained, and the rotating speed variation is considered as a periodic disturbance about this equilibrium condition. Multi-mode discretization of the equations is performed via the spectral Chebyshev approach and the method of multiple scales for gyroscopic systems is employed to study the nonlinear behavior. After determining the required polynomial number based on convergence analysis, results obtained are verified by comparing to those found in literature and numerical simulations. Moreover, the model is validated based on simulations carried out by commercial finite element software. Properties of the functionally graded material and the values of average rotating speed leading to 2:1 internal resonance in the system are found. Time and steady-state responses of the system under primary and parametric resonances caused by the time-dependent rotating speed are investigated when the system is tuned to 2:1 internal resonance. A comprehensive study on the time response, frequency response, and stability behavior shows that the rotating axially functionally graded beam exhibits a complicated nonlinear behavior under the effect of the rotating speed fluctuation frequency, damping coefficient, and properties of the functionally graded material.
This paper presents a novel spectral element method to predict the electromechanical dynamics of panels having arbitrary geometries and multiple surface-bonded piezo-patches. The boundary value problem is derived following kinematic equations based on first order shear deformation and the generalized Hamilton's principle. To solve the derived boundary value problem, a spectral element method based on Chebyshev polynomials is developed. The method combines the flexibility of the finite element method and the accuracy of the meshless methods. Thus, it includes three main parts. First, the whole domain is divided into elements, and then the system matrices for each element is derived using spectral Chebyshev approach. Finally, the individual system matrices are assembled to construct the overall/global system matrices of the investigated structure. The spectral Chebyshev approach enables capturing the structural and electromechanical dynamic behaviour of structures having arbitrary geometries (using a cross-section mapping) and boundary conditions. To demonstrate the performance and validate the accuracy of the presented spectral element method, four case studies are investigated. In each case study, the predicted natural frequencies, structural and voltage FRFs are compared to those obtained from a finite element approach.
In this research a general model to study the vibration behavior of axially moving two-dimensional continuums in the presence of curvature along the moving axis is developed. To this end, an axially moving doubly-curved panel of variable radius of curvature is considered. The integral boundary value problem is obtained based on a higher-order shear deformation with first-order thickness stretching theory. Due to its high accuracy and computational performance, spectral Chebyshev approach is used to numerically solve the boundary value problem. Considering the geometry capabilities of the developed model, dynamics of various axially moving structures such as flat, singly- and doubly-curved plates/shells in different engineering applications with different boundary conditions can be investigated. The numerical results confirmed that the calculated natural frequencies for axially moving flat plates and circular cylindrical shells are in excellent agreement to those found in the literature and obtained via finite element approach. Furthermore, the effects of the axial velocity, thickness stretching, curvature ratio, and boundary conditions on the natural frequencies and stability behavior of the doubly-curved panels are investigated.
This paper presents an electromechanical modeling approach for predicting the dynamics of (straight/curved) functionally graded panels with multiple surface-integrated piezo-patches. Bi-axial material variation is considered using the theory of mixture approach. The governing equations are derived following the first order shear deformation theory and the Hamilton’s principle. The derived boundary value problem is solved numerically using a meshless approach based on Chebyshev polynomials. Mass and stiffness contributions of piezo-patch(es), as well as two-way electromechanical coupling behavior, are incorporated both for modal and harmonic analyses. To validate the accuracy of the presented solution technique, the results for various cases are compared to those obtained from finite-element analyses. It is shown that the maximum difference in the predicted natural frequencies is below 1%, but for a fraction of the computational time. Furthermore, the harmonic analysis results excellently match FE results. Note that material variation changes the spatial stiffness of the panel and thus, the functionally graded panel can be designed according to a predefined objective function using the proposed modeling approach. As a demonstration, specific to energy harvesting application, the voltage/power output was maximized through material and geometry/shape variations. It was demonstrated that significant improvements can be achieved through the presented methodology.
The mechanism of nanoparticle transport inside carbon nanotubes is taken into account to investigate the dynamics of single-walled carbon nanotubes carrying a nanoparticle. The motion of the nanoparticle is on helical tracks, which is induced by temperature difference in the nanotube, with main characteristics such as axial, and angular velocities and pitch angle. The helical motion is modeled based on constrained and unconstrained simulations. In the case of the former, the axial velocity is constant, however, in the latter simulation, the axial velocity is time-variant and stop-and-go events with simultaneous changes in the rotation direction are considered as random uncertainty in the system. Once the helical motion is clarified, the dynamic behavior of the nanotube acted upon by a moving nanoparticle is investigated for simply supported boundary conditions and stability analysis is performed to obtain the critical velocities as well as critical temperature differences based on Floquet theorem. For the case of the system with random uncertainty, the statistical properties as well as confidence and prediction intervals of the dynamic response are also studied by Monte-Carlo simulation. The results highlight the importance of the helical motion mechanism of the moving nanoparticle and the random uncertainty in the system.
This study investigates the vibration and buckling behavior of functionally graded porous composite plates reinforced with graphene platelets (GPLs) using spectral-Tchebychev approach. Buckling strength and vibration behavior depend highly on the dispersion of porosity and nanofiller material along the thickness of the composite plates. The effective material properties are determined based on the volume fractions of the constituent materials. To accurately capture the material gradation, the plate is divided into multiple layers. The governing boundary value problem is derived using first order shear deformation theory (FSDT) and following an energy based approach. To accurately and efficiently solve the boundary value problem, a meshless/spectral method based on Tchebychev polynomials is used. The developed solution approach enables the solution of functionally graded (porous) composite plates under various loading and boundary conditions. To demonstrate the accuracy and the computational performance of the solution approach, two case studies are investigated including composite plates having different porosity distributions and reinforcement amounts. Furthermore, comprehensive parametric studies are carried out to understand how porosity distribution and GPL reinforcements affect the vibration and buckling behavior of composite plates.
Deniz ve hava araçlarında yolcuların transferini sağlamak için geçici köprü sistemi olan geçit merdivenleri (pasarella) kullanılmaktadır. Bu çalışmada fonksiyonel paralel pasarella tasarımı, analizi ve üretimi yapılarak deniz aracına monte edilmiştir. Bu tasarım sayesinde, geleneksel pasarellaların fonksiyonelliğinin ve istiflenmiş verimliliğinin artırılması sağlanarak nispeten daha uzun geçit merdivenleri elde edilmiş ve yer kısıntısı olan yatlara uygulanmasını kolaylaştırılmıştır. Tasarım aşamasında, öncelikle sistemin çubuk mekanizmaları ile kavramsal tasarımı tamamlanmıştır. Ardından 3B modellemenin gerçekleşmesi adına tasarım parametrelerini kolaylıkla elde edebilmek için analitik olarak kinematik analizi yapılmış ve hareket denklemleri MATLAB yardımı ile çözülmüştür. Elde edilen verilere göre sistemin 3B tasarımı bilgisayar destekli tasarım (CAD) programı SolidWorks ile ilgili kurallar (DNVGL-ST-0358) ve uygulanan yatın tasarım limitleri dikkate alınarak modellenmiştir. Modelin statik analizi sonlu elemanlar analizi ANSYS Workbench programı kullanılarak sağlanmıştır. Kompleks tasarımlarda sistemi hareket ettiren eyleyiciler için gerekli kuvvetin hassas bir şekilde hesaplanmasındaki zorluklar nedeni ile ANSYS Katı Cisimler Dinamiği modülü kullanılmış, kuvvet ve kinematik analiz sonuçlarına göre uygun hidrolik pistonlar seçilmiştir. Aynı zamanda analitik olarak elde edilen kinematik analiz sonuçları ANSYS ile doğrulanmıştır. Tasarım isterlerine göre nihai tasarımı yapılan pasarella üretilmiş ve yata uygulanmıştır.
This paper presents an electromechanical model for predicting the dynamics of curved panels with multiple surface-integrated piezo-patches. The boundary value problem governing the electro-elastic dynamic behavior of a (doubly-) curved panel and piezo-patch structure is derived following the first order shear deformation (FSDT) theory. Spectral Tchebychev approach is used to numerically solve the system dynamics and obtain voltage and mechanical frequency response functions (FRFs). Mass and stiffness contributions of piezo-patch(es) as well as two-way electromechanical coupling behavior are incorporated in the model for both modal analysis and frequency response calculations. To validate the accuracy of the developed solution technique, the results for various cases including a single patch and multiple patches on a straight/curved host panel are compared to those obtained from finite-element (FE) analyses. It is shown that the maximum difference in the predicted natural frequencies between the ST and FE results is below 1%, and the harmonic analyses’ results obtained using the presented solution technique excellently match the FE results. Furthermore, the effect of multiple piezoelectric patches to achieve higher voltage values in the application of energy harvesting is investigated when the mode jumping phenomenon occurs due to the increasing curvature.
Efficient modeling and optimization techniques are required to overcome the high design complexity and computational costs concerning the engineering of composite structures. In this paper, a modeling framework for the dynamic analysis of doubly curved composite panels is developed. Lamination parameters are used to characterize the stiffness properties of the laminate, and the responses are calculated through the two-dimensional spectral-Tchebychev method. The proposed framework combines the computational efficiency advantages of both lamination parameters formulation and spectral-Tchebychev method which is extended for dynamic analysis of curved composite laminates. Compared to the finite element method, the developed model significantly decreases the computation duration, thereby leading to analysis speed-ups up to 40 folds. In the case studies, fundamental frequency contours for the doubly curved composite panels are obtained in lamination parameters space for the first time. The results show that, unlike flat or singly curved laminates, the maximum frequency design points for doubly curved panels can be inside the feasible region of lamination parameters requiring multiple layer angles. The fundamental mode shapes for the maximum frequency designs are also computed to investigate the influence of panel curvatures on the vibration patterns, which can exhibit mode switching phenomenon.
This paper describes an efficient framework for the design and optimization of the variable-stiffness composite plates. Equations of motion are solved using a Tchebychev polynomials-based spectral modeling approach that is extended for the classical laminated plate theory. This approach provides highly significant analysis speed-ups with respect to the conventional finite element method. The proposed framework builds on a variable-stiffness laminate design methodology that utilizes lamination parameters for representing the stiffness properties compactly and master node variables for modeling the stiffness variation through distance-based interpolation. The current study improves the existing method by optimizing the locations of the master nodes in addition to their lamination parameter values. The optimization process is promoted by the computationally efficient spectral-Tchebychev solution method. Case studies are performed for maximizing the fundamental frequencies of the plates with different boundary conditions and aspect ratios. The results show that significant improvements can be rapidly achieved compared to optimal constant-stiffness designs by utilizing the developed framework. In addition, the optimization of master node locations resulted in additional improvements in the optimal response values highlighting the importance of including the node positions within the design variables.
The dynamics of micro-scale cutting tools used during micromachining is critical to attainable process precision. Forced and self-excited vibration behavior of a micromachining process depend critically on the dynamic response of the microtools. As these micro tools are rotated at very high speeds (40,000 to 250,000 rpm) the rotational effects can play a critical role in their dynamic response. However, their the complex, multi-dimensional, and pre-twisted geometry causes a coupled dynamic response, thereby rendering the prevailing simplified one-dimensional (1D) modeling approaches inaccurate. Towards addressing this modeling challenge, in this work, we present an application of spectral-Tchebychev (ST) method to predict the three-dimensional (3D) coupled dynamics of microtools including the rotational (gyroscopic) effects. To capture the dynamics of the sectioned geometry of microtools efficiently, a unified modeling approach is followed in the modeling, merging 1D-ST models for the sections having circular cross sections, and 3D-ST models for the fluted section, which exhibits coupled three-dimensional motions due to the complex geometry. The presented solution technique is applied to predict and understand the dynamics of rotating micro-endmills and micro-drills. Natural frequencies, mode shapes, and the frequency response functions (FRFs) obtained from the unified 1D/3D-ST model are shown to have an excellent agreement with those from a commercial finite element (FE) software. The unified 1D/3D-ST model is then used to analyze the accuracy and limitations of reduced-order modeling approaches that could be used to model the rotational dynamics of microtools. Finally, the effect of rotational speed on radial throw arising from the rotational dynamics is investigated.
This paper presents a general electromechanical model for predicting the dynamics of thin or moderately thick plates with surface-integrated piezo-patches. Using spectral Tchebychev (ST) technique, the boundary value problem governing the electroelastic dynamics of the two dimensional (2D) plate and piezo-patch structure is developed with Mindlin plate theory assumptions. Mass and stiffness contributions of piezo-patch(es) as well as two-way electromechanical coupling behavior are incorporated in the model for both modal analysis and frequency response calculations. To validate the accuracy of the developed solution technique, modal analysis results are compared against the existing Rayleigh-Ritz solution from the literature as well as the finite-element simulation results for various piezo-patch sizes on thin and moderately thick host plates; and it is shown that the maximum difference in the predicted natural frequencies between the ST and FE results are below 1\%. The electromechanical frequency response functions (FRFs) including the vibration response and voltage output of the system under a transverse point force excitation are obtained using the ST model and the results are shown to match perfectly with the finite element (FE) simulations. Additionally, comparisons of the electromechanical FRFs calculated based on Rayleigh-Ritz method from the literature versus the developed framework is presented to highlight that the exclusion of shear deformation terms in the former model leads to an inaccurate estimation of electroelastic behavior for the case of thicker plates with surface-bonded piezo-patches. Finally, the investigated case studies demonstrate that the computational efficiency of the developed method is significantly higher than that of FE simulations.
This paper focuses on the dynamics of doubly-curved functionally graded and laminated composite structures with arbitrary geometries and boundary conditions. Integral boundary value problem is obtained following an energy-based approach where the strain energy of the structure is expressed using three-dimensional elasticity equations. The effective properties of functionally graded materials can be described based on Mori-Tanaka or theory of mixtures methods. To simplify the domain of the problem, coordinate transformations are applied to map the curved structure into a straight one; and furthermore, a one-to-one mapping technique is applied to map the (complex) curved geometry to a master geometry in the case of composites with arbitrary geometries. Then, the integral boundary value problem is discretized by means of Gauss-Lobatto sampling and solved using the three-dimensional spectral-Tchebychev approach. In this method, the system matrices are calculated through the exact evaluation of differentiation and integration operations using the derived Tchebychev matrix operators. Finally, if necessary, to impose the essential boundary conditions on the boundary value problem and to assemble multiple layers, the projection matrices approach is used. Various case studies including (i) doubly-curved structures, (ii) doubly-curved laminated composites and (iii) doubly-curved laminated composite structures with arbitrary geometries are analyzed. In each case study, to present the accuracy/precision of the developed solution technique, the predicted (non-dimensional) natural frequencies and mode shapes are compared to those obtained using either a commercial finite element software and/or to those found in literature. It is shown that the developed three-dimensional spectral-Tchebychev solution technique enables accurately and efficiently capturing the vibration behavior of doubly-curved laminated composite structures having arbitrary geometries under different boundary conditions.
This paper presents a new approach, referred to here as the two-dimensional spectral-Tchebychev (2D-ST) technique to predict the dynamics of thick plates having arbitrary geometries under different boundary conditions. The integral boundary value problem governing the dynamics of plate-like structures is obtained using the Mindlin plate theory and following an energy-based approach. To solve the boundary value problem numerically, a spectral-Tchebychev based solution technique is developed. To simplify the calculation of integral and derivative operations and thus to increase the numerical efficiency of the solution approach, a one-to-one coordinate mapping technique is used to map the arbitrary geometry onto an equivalent rectangular in-plane shape of the plate. The proposed solution technique is applied to various different plate problems to assess the accuracy and show the applicability of the technique. In each case, the convergence of the solution is analyzed, and the predicted (non-dimensional) natural frequencies are compared to those found in the literature or to those found using finite element modeling. It is shown that the calculated natural frequencies converge exponentially with increasing number of Tchebychev polynomials used and are in excellent agreement with those found in the literature and found form a finite elements solution. Therefore, it is concluded that the presented spectral-Tchebychev solution technique can accurately and efficiently capture the dynamics of thick plates having arbitrary geometries. Furthermore, the utility of the 2D-ST is demonstrated by comparing the results obtained using a three-dimensional solution approach.
This paper presents the application of the three-dimensional spectral-Tchebychev technique to accurately predict the vibration behavior of bi-directional functionally graded material curved parallelepipeds including geometries such as beams, thin/thick plates, and solids. In this study, the material distribution within the domain of the structure is obtained using bi-directional Mori-Tanaka method. To derive the boundary value problem governing the dynamics of functionally graded curved parallelepipeds, three-dimensional elasticity equations are used together with extended Hamilton’s principle. Numerical solution of the integral boundary value problem is performed using the three-dimensional spectral Tchebychev approach. To validate and assess the performance of the presented solution approach, a number of case studies are conducted. In each case study, the non-dimensional natural frequencies and mode shapes are calculated and compared to those found using a finite element solution approach. Furthermore, computational time of the simulation is measured in each case. It is shown that the presented solution technique enables accurate prediction of vibration behavior of bi-directional functionally graded curved parallelepipeds as precise as a finite elements method, but for a fraction of the computational cost.
This paper presents the application of the spectral-Tchebychev (ST) technique for solution of three-dimensional dynamics of curved beams/structures having variable and arbitrary cross-section under mixed boundary conditions. To accurately capture the vibrational behavior of curved structures, a three-dimensional (3D) solution approach is required since these structures generally exhibit coupled motions. In this study, the integral boundary value problem (IBVP) governing the dynamics of the curved structures is found using extended Hamilton's principle where the strain energy is expressed using 3D linear elasticity equation. To solve the IBVP numerically, the 3D spectral Tchebychev (3D-ST) approach is used. To evaluate the integral and derivative operations defined by the IBVP and to render the complex geometry into an equivalent straight beam with rectangular cross-section, a series of coordinate transformations are applied. To validate and assess the performance of the presented solution approach, two case studies are performed: (i) curved beam with rectangular cross-section, (ii) curved and pretwisted beam with airfoil cross-section. In both cases, the results (natural frequencies and mode shapes) are also found using a finite element (FE) solution approach. It is shown that the difference in predicted natural frequencies are less than 1%, and the mode shapes are in excellent agreement based on the modal assurance criteria (MAC) analyses; however, the presented spectral-Tchebychev solution approach significantly reduces the computational burden. Therefore, it can be concluded that the presented solution approach can capture the 3D vibrational behavior of curved beams as accurately as an FE solution, but for a fraction of the computational cost.
In this paper, we present a comprehensive approach for accurate measurement of high-bandwidth three-dimensional (3D) micromachining forces through dynamic compensation of dynamometers. Accurate measurement of micromachining forces is paramount to gaining fundamental understanding on process mechanics and dynamics of micromachining. Multi-axis dynamometers are used to measure 3D machining forces. However, specified bandwidth of these devices is below the frequencies arising during micromachining while using ultra-high-speed (UHS) spindles. This limitation arises from the effects of the dynamometer's structural dynamics on the measured forces. Therefore, accurate measurement of micromachining forces entails high frequency correction of the signals acquired by the dynamometer by removing the influence of those effects. The presented approach involves: (1) accurate identification of 3D force measurement characteristics of the dynamometer within a 25 kHz bandwidth to capture the effects of the dynamometer dynamics; (2) design of a pseudo-inverse filter-based compensation technique to remove the influence of the dynamic response in 3D; and (3) validation of the compensation technique through custom-devised experiments. Subsequently, the compensation method is applied to the micromilling process to obtain accurate broadband 3D micromachining forces using a miniature multi-axis dynamometer. It is concluded that the presented approach enables accurate determination of 3D micromachining forces. The presented compensation technique is also readily applicable for expanding the bandwidth of large dynamometers.
This paper presents the spectral-Tchebychev (ST) technique for solution of three dimensional (3D) dynamics of rotating structures. In particular, structures that exhibit coupled dynamic response require a 3D modeling approach to capture their dynamic behavior. Rotational motions further complicate this behavior, inducing coriolis, centrifugal softening, and (nonlinear) stress-stiffening effects. Therefore, a 3D solution approach is needed to accurately capture the rotational dynamics. The presented 3D-ST technique provides a fast-converging and precise solution approach for rotational dynamics of structures with complex geometries and mixed boundary conditions. Specifically, unlike finite elements techniques, the presented technique uses a series expansion approach considering distributed-parameter system equations: The integral boundary value problem for rotating structures is discretized using the spectral-Tchebychev approach. To simplify the domain of the structures, cross-sectional and rotational transformations are applied to problems with curved cross-section and pretwisted geometry. The nonlinear terms included in the integral boundary value problem are linearized around an equilibrium solution using the quasi-static method. As a result, mass, damping, and stiffness matrices, as well as a forcing vector, are obtained for a given rotating structure. Several case studies are then performed to demonstrate the application and effectiveness of the 3D-ST solution. For each problem, the natural frequencies and modes shapes from the 3D-ST solution are compared to those from the literature (when available) and to those from a commercial finite elements software. The case studies include rotating/spinning parallelepipeds under free and mixed boundary conditions, and a cantilevered pretwisted beam (i.e., rotating blade) with an airfoil geometry rotating on a hub. It is seen that the natural frequencies and mode shapes from the 3D-ST technique differ from those from the finite elements model by less than 1 percent for any rotational speed; however, 3D-ST approach significantly reduces the computational burden. It is concluded that the 3D-ST technique can be used to obtain the 3D dynamics of rotating structures, including those with mixed boundary conditions and complex geometry, in a precise and numerically efficient fashion.
Micromachining dynamics commonly dictate the attainable accuracy and throughput that can be obtained from micromachining operations. The dynamic behavior of miniature ultra-high-speed (UHS) spindles used in micromachining critically affects micromachining dynamics. As such, there is a strong need for effective techniques to characterize the dynamic behavior of miniature UHS spindles. This paper presents a systematic experimental approach to obtain the speed-dependent two-dimensional dynamics of miniature UHS spindles through experimental modal analysis. A miniature cylindrical artifact with 5 mm overhang is attached to (and rotating with) the spindle to enable providing the dynamic excitations to and measuring the resulting motions of the spindle. A custom-made impact excitation system is used to reproducibly excite the spindle dynamics up to 20 kHz while controlling the impact force. The resulting radial motions of the spindle are measured in two mutually perpendicular directions using two independent fiber-optic laser Doppler vibrometers (LDVs). To ensure the mutual orthogonality of the measurements, the two lasers are aligned precisely using an optical procedure. A frequency-domain filtering approach is used to remove the unwanted spindle motion data from the measurements, thereby isolating the dynamic response. The spindle dynamics is then represented in the form of frequency response functions (FRFs). A global curve-fitting technique is applied to identify natural frequencies and damping ratios. The developed approach is demonstrated on a miniature UHS spindle with aerodynamic bearings, and dynamic characteristics are analyzed at different spindle speeds and collet pressures. The spindle speed is shown to have a significant effect on dynamic response, especially at higher spindle speeds, while the collet pressure is observed not to have any significant effect on the spindle dynamics. It is concluded that the presented approach can be used to characterize the dynamics of miniature UHS spindles effectively.
Miniature components and devices are increasingly seen in a myriad of applications. In general, the dynamic behavior of miniature devices is critical to their functionality and performance. However, modal testing of miniature structures poses many challenges. This paper presents a design and evaluation of an impact excitation system (IES) for repeatable, high-bandwidth, controlled-force modal testing of miniature structures. Furthermore, a dynamic model of the system is derived and experimentally validated to enable the identification of the system parameters that yield single-hit impacts with desired bandwidth and force magnitude. The system includes a small instrumented impact tip attached to a custom designed flexure-based body, an automated electromagnetic release mechanism, and various precision positioners. The excitation bandwidth and the impact force magnitude can be controlled by selecting the system parameters. The dynamic model of the system includes the structural dynamics of the flexure-based body, the electromagnetic force and the associated eddy-current damping, and the impact event. A validation study showed an excellent match between the model simulations and experiments in terms of impact force and bandwidth. The model is then used to create process maps that relate the system parameters to the number of hits (single vs. multiple), the impact force magnitudes and the excitation bandwidths. These process maps can be used to select system parameters or predict system response for a given set of parameters. A set of experiments is conducted to compare the performances of the IES and a (manual) miniature impact hammer. It is concluded that the IES significantly improves repeatability in terms of the impact bandwidth, location, and force magnitude, while providing a high excitation-bandwidth and excellent coherence values. The application of the IES is demonstrated through modal testing of a miniature contact-probe system.
This paper presents the application of the spectral-Tchebychev (ST) technique for solution of three-dimensional dynamics of unconstrained pretwisted beams with general cross-section (including both straight and curved cross-sections). In general, the dynamic response of pretwisted beams presents three-dimensional (3D) motions, including coupled bending–bending–torsional–axial motions. As such, accurately solving pretwisted beam dynamics requires a 3D solution approach. In this work, the integral boundary value problem based on the 3D linear elasticity equations is solved numerically using the 3D-ST approach. To simplify evaluation of the volume integrals, the boundaries are simplified by applying two coordinate transformations to render the pretwisted beam with curved cross-section into an equivalent straight beam with rectangular cross-section. Three sample pretwisted beam problems with rectangular, curved, and airfoil cross-sections at different twist rates are solved using the presented approach. In each case, the convergence of the solution is analyzed, and non-dimensional natural frequencies and mode shapes are compared to those from a finite-element (FE) solution. Furthermore, cross-sectional stress and displacements are obtained from the 3D-ST solution. Lastly, the non-dimensional natural frequencies from the 3D-ST and a 1D/2D solutions are compared. It is concluded that the 3D-ST solution can capture the three-dimensional dynamic behavior of pretwisted beams as accurately as an FE solution, but for a fraction of the computational cost. Furthermore, it is shown that 1D/2D solution can lead to significant errors at high twist rates, and thus, the 3D-ST solution should be preferred.
In this paper, we present a comprehensive technique for accurate determination of three-dimensional (3D) dynamic force measurement characteristics of multi-axis dynamometers within a broad range of frequencies. Many research and development efforts in machining science and technology rely upon being able to make precise measurements of machining forces. In micromachining and high-speed machining, cutting forces include components at frequencies significantly higher than the bandwidth of force dynamometers. Further, the machining forces are three-dimensional in nature. This paper presents a new experimental technique to determine the three-dimensional force-measurement characteristics of multi-axis dynamometers. A custom-designed artifact is used to facilitate applying impulsive forces to the dynamometer at different positions in three dimensions. Repeatable and high-quality impulse excitations are provided from a novel impact excitation system with a bandwidth above 25 kHz. The force measurement characteristics are presented within 25 kHz bandwidth using 3 × 3 force-to-force frequency response functions (F2F-FRFs), which capture both direct and dynamic cross-talk components to enable fully three-dimensional characterization. The presented approach is used to characterize the dynamic behavior of a three-axis miniature dynamometer. The effects of force-application position, artifact geometry, and dynamometer-fixturing conditions are explored. Moreover, the relationship between the force-measurement characteristics and structural dynamics of the dynamometer assembly is analyzed. It is concluded that the presented technique is effective in determining the force-measurement characteristics of multi-axis dynamometers. The changes in dynamometer assembly that affect its structural dynamics, including artifact (workpiece) geometry and especially the fixturing conditions, were seen to have a significant effect on force-measurement characteristics. Furthermore, the force-measurement characteristics were seen to change substantially with the force-application position. The presented technique provides a foundation for future compensation efforts to enable measuring forces within a broad range of frequencies.
Design and evaluate a new micro-machining based approach for fabricating dissolvable microneedle arrays (MNAs) with diverse geometries and from different materials for dry delivery to skin microenvironments. The aims are to describe the new fabrication method, to evaluate geometric and material capability as well as reproducibility of the method, and to demonstrate the effectiveness of fabricated MNAs in delivering bioactive molecules.
Precise master molds were created using micromilling. Micromolding was used to create elastomer production molds from master molds. The dissolvable MNAs were then fabricated using the spin-casting method. Fabricated MNAs with different geometries were evaluated for reproducibility. MNAs from different materials were fabricated to show material capability. MNAs with embedded bioactive components were tested for functionality on human and mice skin.
MNAs with different geometries and from carboxymethyl cellulose, polyvinyl pyrrolidone and maltodextrin were created reproducibly using our method. MNAs successfully pierce the skin, precisely deliver their bioactive cargo to skin and induce specific immunity in mice.
We demonstrated that the new fabrication approach enables creating dissolvable MNAs with diverse geometries and from different materials reproducibly. We also demonstrated the application of MNAs for precise and specific delivery of biomolecules to skin microenvironments in vitro and in vivo.
This article investigates the feasibility of using supercritical carbon dioxide based metalworking fluids (scCO2 metalworking fluids (MWFs)) to improve micromachinability of metals. Specifically, sets of channels were fabricated using micromilling on 304 stainless steel and 101 copper under varying machining conditions with and without scCO2 MWF. Burr formation, average specific cutting energy, surface roughness, and tool wear were analyzed and compared. Compared to dry machining, use of scCO2 MWF reduced burr formation in both materials, reduced surface roughness by up to 69% in 304 stainless steel and up to 33% in 101 copper, tool wear by up to 20% in 101 copper, and specific cutting energy by up to 87% in 304 stainless steel and up to 40% in 101 copper. The results demonstrate an improvement in micromachinability of the materials under consideration and motivate future investigations of scCO2 MWF-assisted micromachining to reveal underlying mechanisms of functionality, as well as to directly compare the performance of scCO2 MWF with alternative MWFs appropriate for micromachining.
Vibration behavior of structures with parallelepiped shape—including beams, plates, and solids—are critical for a broad range of practical applications. In this paper we describe a new approach, referred to here as the three-dimensional spectral-Tchebychev (3D-ST) technique, for solution of three-dimensional vibrations of parallelepipeds with different boundary conditions. An integral form of the boundary-value problem is derived using the extended Hamilton’s principle. The unknown displacements are then expressed using a triple expansion of scaled Tchebychev polynomials, and analytical integration and differentiation operators are replaced by matrix operators. The boundary conditions are incorporated into the solution through basis recombination, allowing the use of the same set of Tchebychev functions as the basis functions for problems with different boundary conditions. As a result, the discretized equations of motion are obtained in terms of mass and stiffness matrices. To analyze the numerical convergence and precision of the 3D-ST solution, a number of case studies on beams, plates, and solids with different boundary conditions have been conducted. Overall, the calculated natural frequencies were shown to converge exponentially with the number of polynomials used in the Tchebychev expansion. Furthermore, the natural frequencies and mode shapes were in excellent agreement with those from a finite-element solution. It is concluded that the 3D-ST technique can be used for accurate and numerically efficient solution of three-dimensional parallelepiped vibrations under mixed boundary conditions.
This paper presents a model for the three-dimensional (3D) dynamic response of endmills while considering the actual fluted cross-sectional geometry and pretwisted shape of the tools. The model is solved using the spectral-Tchebychev (ST) technique. The bending and the coupled torsional-axial behavior of four different fluted endmills is compared to finite element model (FEM) predictions and experimental results obtained using modal testing under free-free boundary conditions. For the first eight modes, including six bending and two torsional/axial modes, the difference between the 3D-ST and experimental natural frequencies is shown to be 3% or less for all four tools tested during this study. For the same modes, the 3D-ST and FEM predictions agree to better than 1%. To demonstrate its application, the 3D-ST model for the fluted section of a commercial endmill is coupled to the spindle–holder to predict the tool-point dynamics using receptance coupling substructure analysis (RCSA) with a flexible connection. The coupled model is validated through experiments.
Vibration analysis is a promising technique in diagnosing metabolic bone diseases such as osteoporosis and monitoring fracture healing. The aim of this study is to observe the structural dynamic property changes of the tibia extracted from the vibration analysis data.
In this study, bone mineral density and vibration measurements were made both in in vivo and in vitro conditions. The relationship between structural dynamic properties, obtained and bone mineral densities measured were investigated. Also, the effect of soft tissues on measured structural dynamic properties was analyzed.
Natural frequency of the tibia decreased with decreasing bone mineral density that presented a weak correlation with the bone mineral density values measured by dual energy X-ray densitometer of the femur. In the case of in vitro experiments, it was observed that the effect of muscles on measurement results is higher than that of the effect of the skin and the fibula which makes the modal identification procedure difficult. However, having very large percentage changes in the loss factors when mineral content and collagen are reduced is an encouraging result to believe that damping measurements may yield a promising technique in diagnosing progressing osteoporosis and monitoring fracture healing period.
The utilization of natural frequency alone as a diagnosing tool does not seem to be a sufficient method although there is a correlation between this parameter and bone mineral density. However, in vitro experiments showed that the identification of the loss factor is a promising technique in diagnosing progressing osteoporosis.
In this paper, we present a comprehensive technique to obtain accurate three-dimensional (3D) micromachining forces for frequency bandwidths up to 25 kHz. The capability to precisely measure cutting forces is central to gaining fundamental understanding on micromachining mechanics and dynamics. Multi-axis dynamometers are used to measure 3D machining forces. Forces experienced during micromachining involve very high frequencies due to the ultra-high spindle speeds used during the process. However, the specified bandwidths of the dynamometers do not meet high frequency requirements of micromachining forces; this limitation stems from the structural-dynamics response of the dynamometers. Therefore, it is important to develop approaches to compensate for the distortions arising from the dynamic effects of the dynamometer's structure in order to accurately measure micromachining forces. This paper presents a fully 3D compensation approach to enable accurate determination of 3D micromachining forces within a wide frequency range. The presented approach involves: (1) accurate identification of 3D force measurement characteristics of the dynamometer in the form of 3x3 force-to-force frequency response functions (F2F-FRFs) matrix within a 25 kHz bandwidth, (2) design of an optimal inverse filter for post-processing the measured force data to remove the influence of structural dynamics of the dynamometer; and (3) validation of the compensation approach through impact testing where the actual applied force data acquired by the reference force sensor is compared with the corrected dynamometer measurements. Subsequently, the presented approach is demonstrated by obtaining 3D micromachining forces during micromilling of a brass workpiece. It is concluded that the presented approach is effective in high-frequency correction of dynamometer measurements for accurate measurement of 3D micromachining forces within the 0- 25 kHz frequency range.
This course is designed for undergraduate students to develop the ability to evaluate engineering problems under static loading conditions through drawing free body diagrams, calculating internal and reaction forces using equations of equilibrium.
This course is designed both for undergraduate and graduate students. It is aimed to teach the fundamental concepts how systems vibrate. Fundamental aspects of vibrations for mathematical modeling, derivation/solution of equations of motion, and subsequent system analysis will be covered for discrete systems.
This course is designed for graduate students. It is aimed to teach the fundamental concepts how continuous systems vibrate. Fundamental aspects of vibrations for mathematical modeling, derivation/solution of boundary value problem, and subsequent system analysis will be covered both using analytical and approximate methods..
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