Seyed M. Hashemi - Academia.edu (original) (raw)
Papers by Seyed M. Hashemi
WIT Transactions on the Built Environment, May 28, 2003
The small linear harmonic oscillations of linearly elastic coupled beam structures are addressed.... more The small linear harmonic oscillations of linearly elastic coupled beam structures are addressed. The Finite Element Method (FEM), conventional Hermite beam formulation, and the resulting element matrices are then briefly discussed. The so-called exact Dynamic Stiffness Matrix (DSM) formulation for the longitudinal vibration of axially loaded beams is presented. Finally, the Dynamic Finite Element (DFE) approach is introduced and its application to the axial vibration of beams is displayed. The comparison is made between the standard static and (frequency dependent) Dynamic beam shape functions. The DFE formulation, combines the generality of the FEM and the high precision provided by DSM methods. The weighting functions and shape functions are evaluated referring to the appropriate exact DSM formulation. The DFE approach can be advantageously extended to more complex cases which distinguishes this method from the DSM method.
Aerospace
Finite Element Analysis (FEA) is a powerful tool that can aid in the engineering design process t... more Finite Element Analysis (FEA) is a powerful tool that can aid in the engineering design process to reduce cost and time. However, it is best used in conjunction with experimental data, through which its numerical results can be verified. This paper presents the experimental and numerical modal analyses of an experimental rocket aerostructure to verify the accuracy of the numerical models. This aerostructure has been through flight loads and a recovery. The first numerical results for the rocket showed a 96% difference with the experimental ones. Subsequently, three mass refinements were made to create calibrated FEM models whose results differed from the experimental ones by 19% to 8%. Additionally, as expected, the FEM results tended to overestimate the stiffness of structures. The numerical simulations for all components were performed through ANSYS software, and the experiments were conducted using the hammer tap test with laser vibrometers as sensors.
Metals
The present study aims to investigate the interaction of ratcheting and fatigue phenomena for add... more The present study aims to investigate the interaction of ratcheting and fatigue phenomena for additively manufactured (AM) samples of SS304L and AlSi10Mg undergoing uniaxial asymmetric stress cycles. Overall damage was accumulated through fatigue and ratcheting on AM samples prepared from three-dimensional-printed plates along vertical and horizontal directions. Fatigue damage was evaluated based on the strain energy density fatigue approach and ratcheting damage was calculated through use of an isotropic–kinematic hardening framework. The isotropic description through the Lee–Zavrel (L–Z) model formed the initial and concentric expansion of yield surfaces while the Ahmadzadeh–Varvani (A–V) kinematic hardening rule translated yield surfaces into the deviatoric stress space. Ratcheting of AM samples was simulated using finite element analysis through use of triangular and quadrilateral elements. Ratcheting values of the AM samples were simulated on the basis of Chaboche’s materials m...
Aerospace
Aircraft experience various phases during each flight. Optimal performance, without compromise, d... more Aircraft experience various phases during each flight. Optimal performance, without compromise, during various phases can be achieved through adaptability in the wing design. Morphing wing design encompasses most, if not all, the flight conditions variations, and can respond interactively. In the present work, the dynamic characteristics of a reconfigurable modular morphing wing of two topological architectures, developed in-house by a research group at Toronto Metropolitan University (formerly Ryerso University), were investigated. This modular morphing wing, developed based on the idea of a parallel robot, consists of a number of structural elements connected to each other and to the wing ribs through eye-bolt joints. Euler–Bernoulli and Timoshenko bending beam theories, in conjunction with Finite Element Analysis, were exploited. Free vibration of unmorphed (Original) and morphed configurations subjected to spanwise extensions were studied. The results of systems’ free vibration ...
Aerospace
Detrimental environmental impacts due to the increasing demands of the aviation industry have gai... more Detrimental environmental impacts due to the increasing demands of the aviation industry have gained tremendous global attention. With a potential fuel saving, along with high aerodynamic performance and maneuverability during different phases of a flight, adaptable wing design has become a viable alternative to its fixed-shape counterpart. A morphing wing design embraces, and can respond accordingly to, most of the flight condition variations effectively and efficiently. Despite these prospects, morphing wing design comes with some challenges due to its inherent complexity caused by an increased number of degrees of freedom. With the availability of various morphing parameters, the vibration signature of a morphing wing design plays a vital role in terms of its structural as well as aeroelastic characteristics. In the present paper, the dynamic characteristics of a re-configurable modular morphing wing developed in-house by a research team at Toronto Metropolitan University are inv...
Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 2012
The unsteady aerodynamics of a pair of multi-plunging airfoils is studied using computational flu... more The unsteady aerodynamics of a pair of multi-plunging airfoils is studied using computational fluid dynamics based on a finite volume method and dynamic layering mesh motion algorithm. The two-dimensional unsteady, incompressible Navier–Stokes equations are used as the governing equations while the thin ellipsoidal airfoils, commonly used in micro aerial vehicles, perform harmonic plunging motion. The instantaneous lift and drag coefficients are examined in detail and the effects of Reynolds number, frequency and amplitude of oscillations, and the airfoils’ centre-to-centre spacing on the force coefficients are investigated. It is shown that the force coefficients of each of the plunging airfoils differ noticeably from those of a single plunging airfoil both quantitatively and qualitatively, showing the significance of the airfoil–airfoil interaction. It is also observed that the investigated parameters affect the magnitude and characteristics of the real-time lift and drag coeffici...
ASME 2010 3rd Joint US-European Fluids Engineering Summer Meeting: Volume 1, Symposia – Parts A, B, and C, 2010
The objective of the present study is to investigate the low Reynolds number (LRN) fluid dynamics... more The objective of the present study is to investigate the low Reynolds number (LRN) fluid dynamics of an elliptic airfoil performing a novel figure-eight-like motion. To this mean, the influence of phase angle between the pitching and translational (heaving and lagging) motions and the amplitude of translational motions on the fluid flow is simulated. Navier-Stokes (NS) equations with Finite Volume Method (FVM) are used and the instantaneous force coefficients and the fluid dynamics performance, as well as the corresponding vortical structures are analyzed. Both the phase angle and the amplitudes of horizontal and vertical motions are of great importance to the fluid dynamic characteristics of the model as they are shown to change the peaks of the fluid forces, fluid dynamic performance, and the vortical patterns around the model.Copyright © 2010 by ASME
40th Fluid Dynamics Conference and Exhibit, 2010
The objective of the present study is to simulate the low Reynolds number (LRN) fluid dynamics of... more The objective of the present study is to simulate the low Reynolds number (LRN) fluid dynamics of a two-dimensional (2-D) elliptic airfoil performing a novel figure-eight-like motion. To this end, the influence of Reynolds number (Re) and amplitude of pitching motion on the fluid flow is investigated. Navier-Stokes (N-S) equations are solved using a Finite Volume Method (FVM), and the instantaneous lift and drag coefficients and the corresponding vortical structures are analyzed. The results show that both Re and the amplitude of pitching oscillations have great influence on the fluid dynamics characteristics of the flapping airfoil.
Journal of Fluids and Structures, 2011
The flow field of a flapping airfoil in Low Reynolds Number (LRN) flow regime is associated with ... more The flow field of a flapping airfoil in Low Reynolds Number (LRN) flow regime is associated with complex nonlinear vortex shedding and viscous phenomena. The respective fluid dynamics of such a flow is investigated here through Computational Fluid Dynamics (CFD) based on the Finite Volume Method (FVM). The governing equations are the unsteady, incompressible two-dimensional Navier-Stokes (N-S) equations. The airfoil is a thin ellipsoidal geometry performing a modified figure-of-eight-like flapping pattern. The flow field and vortical patterns around the airfoil are examined in detail, and the effects of several unsteady flow and system parameters on the flow characteristics are explored. The investigated parameters are the amplitude of pitching oscillations, phase angle between pitching and plunging motions, mean angle of attack, Reynolds number (Re), Strouhal number (St) based on the translational amplitudes of oscillations, and the pitching axis location (x/c). It is shown that these parameters change the instantaneous force coefficients quantitatively and qualitatively. It is also observed that the strength, interaction, and convection of the vortical structures surrounding the airfoil are significantly affected by the variations of these parameters.
Aerospace
Growing concerns over the CO2 footprint due the exponential demand of the aviation industry, alon... more Growing concerns over the CO2 footprint due the exponential demand of the aviation industry, along with the requirements for high aerodynamic performance, cost saving, and manoeuvrability during different phases of a flight, pave the path towards adaptable wing design. Morphing wing design encompasses most, if not all, of the flight condition variations, and can respond interactively. However, functional failure of the morphing wing might bring devastating impacts on the passengers, crew, and/or aircraft. In the present work, the dynamic characteristics of a re-configurable modular morphing wing developed in-house by a research group at the Toronto Metropolitan University, are investigated from the perspective of a functional hazard assessment (FHA). This modular morphing wing, developed based on the idea of a parallel robot, consists of a number of structural elements connected to each other and to the wing ribs through eye-bolt joints. Timoshenko’s bending beam theory, in conjunct...
This work presents the bending–torsion coupled free vibration analysis of prestressed, layered co... more This work presents the bending–torsion coupled free vibration analysis of prestressed, layered composite beams subjected to axial force and end moment using the traditional finite element method (FEM) and dynamic finite element (DFE) techniques. Current trends in the literature, in terms of different types of modeling techniques and constraints, were briefly examined. The Galerkin-type weighted residual method was applied to convert the coupled differential equations of motion into a discrete problem using a polynomial interpolation function in the finite element method. In the dynamic finite element method, trigonometric shape functions were implemented to describe the equations in terms of nodal displacements. The eigenvalue problem resulting from the discretization along the length of the beam was solved in order to determine the system’s natural frequencies and modes. The results, showing the effects of axial load, end moment, and combined loading on natural frequencies, are dis...
International Journal of Aerospace Engineering, 2009
An airfoil subjected to two-dimensional incompressible inviscid flow is considered. The airfoil i... more An airfoil subjected to two-dimensional incompressible inviscid flow is considered. The airfoil is supported via a translational and a torsional springs. The aeroelastic integro-differential equations of motion for the airfoil are reformulated into a system of six first-order autonomous ordinary differential equations. These are the simplest and least number of ODEs that can present this aeroelastic system. The differential equations are then used for the bifurcation analysis of an airfoil with a structural nonlinearity in the pitch direction. Sample bifurcation diagrams showing both stable and unstable limit cycle oscillation are presented. The types of bifurcations are assessed by evaluating the Floquet multipliers. For a specific case, a period doubling route to chaos was detected, and mildly chaotic behavior in a narrow range of velocity was confirmed via the calculation of the Lyapunov exponents.
Volume 3: 19th International Conference on Design Theory and Methodology; 1st International Conference on Micro- and Nanosystems; and 9th International Conference on Advanced Vehicle Tire Technologies, Parts A and B, 2007
MEMS parallel-plate tunable capacitors are widely used in different areas such as tunable filters... more MEMS parallel-plate tunable capacitors are widely used in different areas such as tunable filters, resonators and communications (RF) systems for their simple structures, high Q-factors and small sizes. However, these capacitors have relatively low tuning range (50%) and are subjected to highly sensitive and nonlinear capacitance-voltage (C-V) responses. In this paper novel designs are developed which have C-V responses with high linearity and tunability and low sensitivity. The designs use the flexibility of the moving plates. The plate is segmented to provide a controllable flexibility. Segments are connected together at end nodes by torsional springs. Under each node there is a step which limits the vertical movement of that node. An optimization program finds the best set of step heights that provides the highest linearity. Two numerical examples of three-segmented- and six-segmented-plate capacitors verify that the segmentation of moving plate can considerably improve the linea...
48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 2007
A frequency-dependent, Dynamic Finite Element (DFE) formulation is developed to study the coupled... more A frequency-dependent, Dynamic Finite Element (DFE) formulation is developed to study the coupled flexural–torsional vibration of a preloaded, linearly elastic, slender beam subjected to an axial load and end moment. Euler-Bernoulli bending and St. Venant torsion beam theories are used to develop the governing equations and the DFE solution. A nonlinear Eigenvalue problem is formulated and the Eigensolutions are determined using a dedicated Matlab ® code. The DFE frequency results, for an illustrative example, are validated against conventional Finite Element Method (FEM). Various classical boundary conditions and loadings are considered. As expected, tensile forces increase natural frequencies indicating beam stiffening, compared to compressive forces that reduce the beams stiffness, seen by a reduction in natural frequency. When a force and an end moment are acting in combination, the moment reduces the stiffness of the beam. Nevertheless, the stiffness of the beam is found to be ...
Volume 4: 20th International Conference on Design Theory and Methodology; Second International Conference on Micro- and Nanosystems, 2008
In conventional MEMS parallel-plate capacitor designs, the moving electrode is commonly modeled a... more In conventional MEMS parallel-plate capacitor designs, the moving electrode is commonly modeled as a rigid plate with flexible boundary conditions provided by a set of supporting beams. Such a capacitor generates limited tuning ratio up to 1.5 and its capacitance-voltage response is nonlinear. This paper presents novel designs where the moving electrodes are fixed-edge flexible plates. The plate displacement is selectively limited by a set of rigid steps, located between two electrodes, to generate a smooth and linear response and high tunability. Three different step heights are considered in the design and the linearity of the C-V curve is maximized by modifying the geometry of the plate, and changing the location and order of steps. Since the analytical solution for coupled electrostatic-structural physics in this case does not exist, ANSYS® FEM simulation is performed to obtain the C-V curves and optimize the design. Two designs with different electrode shapes, rectangular and c...
WIT Transactions on the Built Environment, May 28, 2003
The small linear harmonic oscillations of linearly elastic coupled beam structures are addressed.... more The small linear harmonic oscillations of linearly elastic coupled beam structures are addressed. The Finite Element Method (FEM), conventional Hermite beam formulation, and the resulting element matrices are then briefly discussed. The so-called exact Dynamic Stiffness Matrix (DSM) formulation for the longitudinal vibration of axially loaded beams is presented. Finally, the Dynamic Finite Element (DFE) approach is introduced and its application to the axial vibration of beams is displayed. The comparison is made between the standard static and (frequency dependent) Dynamic beam shape functions. The DFE formulation, combines the generality of the FEM and the high precision provided by DSM methods. The weighting functions and shape functions are evaluated referring to the appropriate exact DSM formulation. The DFE approach can be advantageously extended to more complex cases which distinguishes this method from the DSM method.
Aerospace
Finite Element Analysis (FEA) is a powerful tool that can aid in the engineering design process t... more Finite Element Analysis (FEA) is a powerful tool that can aid in the engineering design process to reduce cost and time. However, it is best used in conjunction with experimental data, through which its numerical results can be verified. This paper presents the experimental and numerical modal analyses of an experimental rocket aerostructure to verify the accuracy of the numerical models. This aerostructure has been through flight loads and a recovery. The first numerical results for the rocket showed a 96% difference with the experimental ones. Subsequently, three mass refinements were made to create calibrated FEM models whose results differed from the experimental ones by 19% to 8%. Additionally, as expected, the FEM results tended to overestimate the stiffness of structures. The numerical simulations for all components were performed through ANSYS software, and the experiments were conducted using the hammer tap test with laser vibrometers as sensors.
Metals
The present study aims to investigate the interaction of ratcheting and fatigue phenomena for add... more The present study aims to investigate the interaction of ratcheting and fatigue phenomena for additively manufactured (AM) samples of SS304L and AlSi10Mg undergoing uniaxial asymmetric stress cycles. Overall damage was accumulated through fatigue and ratcheting on AM samples prepared from three-dimensional-printed plates along vertical and horizontal directions. Fatigue damage was evaluated based on the strain energy density fatigue approach and ratcheting damage was calculated through use of an isotropic–kinematic hardening framework. The isotropic description through the Lee–Zavrel (L–Z) model formed the initial and concentric expansion of yield surfaces while the Ahmadzadeh–Varvani (A–V) kinematic hardening rule translated yield surfaces into the deviatoric stress space. Ratcheting of AM samples was simulated using finite element analysis through use of triangular and quadrilateral elements. Ratcheting values of the AM samples were simulated on the basis of Chaboche’s materials m...
Aerospace
Aircraft experience various phases during each flight. Optimal performance, without compromise, d... more Aircraft experience various phases during each flight. Optimal performance, without compromise, during various phases can be achieved through adaptability in the wing design. Morphing wing design encompasses most, if not all, the flight conditions variations, and can respond interactively. In the present work, the dynamic characteristics of a reconfigurable modular morphing wing of two topological architectures, developed in-house by a research group at Toronto Metropolitan University (formerly Ryerso University), were investigated. This modular morphing wing, developed based on the idea of a parallel robot, consists of a number of structural elements connected to each other and to the wing ribs through eye-bolt joints. Euler–Bernoulli and Timoshenko bending beam theories, in conjunction with Finite Element Analysis, were exploited. Free vibration of unmorphed (Original) and morphed configurations subjected to spanwise extensions were studied. The results of systems’ free vibration ...
Aerospace
Detrimental environmental impacts due to the increasing demands of the aviation industry have gai... more Detrimental environmental impacts due to the increasing demands of the aviation industry have gained tremendous global attention. With a potential fuel saving, along with high aerodynamic performance and maneuverability during different phases of a flight, adaptable wing design has become a viable alternative to its fixed-shape counterpart. A morphing wing design embraces, and can respond accordingly to, most of the flight condition variations effectively and efficiently. Despite these prospects, morphing wing design comes with some challenges due to its inherent complexity caused by an increased number of degrees of freedom. With the availability of various morphing parameters, the vibration signature of a morphing wing design plays a vital role in terms of its structural as well as aeroelastic characteristics. In the present paper, the dynamic characteristics of a re-configurable modular morphing wing developed in-house by a research team at Toronto Metropolitan University are inv...
Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 2012
The unsteady aerodynamics of a pair of multi-plunging airfoils is studied using computational flu... more The unsteady aerodynamics of a pair of multi-plunging airfoils is studied using computational fluid dynamics based on a finite volume method and dynamic layering mesh motion algorithm. The two-dimensional unsteady, incompressible Navier–Stokes equations are used as the governing equations while the thin ellipsoidal airfoils, commonly used in micro aerial vehicles, perform harmonic plunging motion. The instantaneous lift and drag coefficients are examined in detail and the effects of Reynolds number, frequency and amplitude of oscillations, and the airfoils’ centre-to-centre spacing on the force coefficients are investigated. It is shown that the force coefficients of each of the plunging airfoils differ noticeably from those of a single plunging airfoil both quantitatively and qualitatively, showing the significance of the airfoil–airfoil interaction. It is also observed that the investigated parameters affect the magnitude and characteristics of the real-time lift and drag coeffici...
ASME 2010 3rd Joint US-European Fluids Engineering Summer Meeting: Volume 1, Symposia – Parts A, B, and C, 2010
The objective of the present study is to investigate the low Reynolds number (LRN) fluid dynamics... more The objective of the present study is to investigate the low Reynolds number (LRN) fluid dynamics of an elliptic airfoil performing a novel figure-eight-like motion. To this mean, the influence of phase angle between the pitching and translational (heaving and lagging) motions and the amplitude of translational motions on the fluid flow is simulated. Navier-Stokes (NS) equations with Finite Volume Method (FVM) are used and the instantaneous force coefficients and the fluid dynamics performance, as well as the corresponding vortical structures are analyzed. Both the phase angle and the amplitudes of horizontal and vertical motions are of great importance to the fluid dynamic characteristics of the model as they are shown to change the peaks of the fluid forces, fluid dynamic performance, and the vortical patterns around the model.Copyright © 2010 by ASME
40th Fluid Dynamics Conference and Exhibit, 2010
The objective of the present study is to simulate the low Reynolds number (LRN) fluid dynamics of... more The objective of the present study is to simulate the low Reynolds number (LRN) fluid dynamics of a two-dimensional (2-D) elliptic airfoil performing a novel figure-eight-like motion. To this end, the influence of Reynolds number (Re) and amplitude of pitching motion on the fluid flow is investigated. Navier-Stokes (N-S) equations are solved using a Finite Volume Method (FVM), and the instantaneous lift and drag coefficients and the corresponding vortical structures are analyzed. The results show that both Re and the amplitude of pitching oscillations have great influence on the fluid dynamics characteristics of the flapping airfoil.
Journal of Fluids and Structures, 2011
The flow field of a flapping airfoil in Low Reynolds Number (LRN) flow regime is associated with ... more The flow field of a flapping airfoil in Low Reynolds Number (LRN) flow regime is associated with complex nonlinear vortex shedding and viscous phenomena. The respective fluid dynamics of such a flow is investigated here through Computational Fluid Dynamics (CFD) based on the Finite Volume Method (FVM). The governing equations are the unsteady, incompressible two-dimensional Navier-Stokes (N-S) equations. The airfoil is a thin ellipsoidal geometry performing a modified figure-of-eight-like flapping pattern. The flow field and vortical patterns around the airfoil are examined in detail, and the effects of several unsteady flow and system parameters on the flow characteristics are explored. The investigated parameters are the amplitude of pitching oscillations, phase angle between pitching and plunging motions, mean angle of attack, Reynolds number (Re), Strouhal number (St) based on the translational amplitudes of oscillations, and the pitching axis location (x/c). It is shown that these parameters change the instantaneous force coefficients quantitatively and qualitatively. It is also observed that the strength, interaction, and convection of the vortical structures surrounding the airfoil are significantly affected by the variations of these parameters.
Aerospace
Growing concerns over the CO2 footprint due the exponential demand of the aviation industry, alon... more Growing concerns over the CO2 footprint due the exponential demand of the aviation industry, along with the requirements for high aerodynamic performance, cost saving, and manoeuvrability during different phases of a flight, pave the path towards adaptable wing design. Morphing wing design encompasses most, if not all, of the flight condition variations, and can respond interactively. However, functional failure of the morphing wing might bring devastating impacts on the passengers, crew, and/or aircraft. In the present work, the dynamic characteristics of a re-configurable modular morphing wing developed in-house by a research group at the Toronto Metropolitan University, are investigated from the perspective of a functional hazard assessment (FHA). This modular morphing wing, developed based on the idea of a parallel robot, consists of a number of structural elements connected to each other and to the wing ribs through eye-bolt joints. Timoshenko’s bending beam theory, in conjunct...
This work presents the bending–torsion coupled free vibration analysis of prestressed, layered co... more This work presents the bending–torsion coupled free vibration analysis of prestressed, layered composite beams subjected to axial force and end moment using the traditional finite element method (FEM) and dynamic finite element (DFE) techniques. Current trends in the literature, in terms of different types of modeling techniques and constraints, were briefly examined. The Galerkin-type weighted residual method was applied to convert the coupled differential equations of motion into a discrete problem using a polynomial interpolation function in the finite element method. In the dynamic finite element method, trigonometric shape functions were implemented to describe the equations in terms of nodal displacements. The eigenvalue problem resulting from the discretization along the length of the beam was solved in order to determine the system’s natural frequencies and modes. The results, showing the effects of axial load, end moment, and combined loading on natural frequencies, are dis...
International Journal of Aerospace Engineering, 2009
An airfoil subjected to two-dimensional incompressible inviscid flow is considered. The airfoil i... more An airfoil subjected to two-dimensional incompressible inviscid flow is considered. The airfoil is supported via a translational and a torsional springs. The aeroelastic integro-differential equations of motion for the airfoil are reformulated into a system of six first-order autonomous ordinary differential equations. These are the simplest and least number of ODEs that can present this aeroelastic system. The differential equations are then used for the bifurcation analysis of an airfoil with a structural nonlinearity in the pitch direction. Sample bifurcation diagrams showing both stable and unstable limit cycle oscillation are presented. The types of bifurcations are assessed by evaluating the Floquet multipliers. For a specific case, a period doubling route to chaos was detected, and mildly chaotic behavior in a narrow range of velocity was confirmed via the calculation of the Lyapunov exponents.
Volume 3: 19th International Conference on Design Theory and Methodology; 1st International Conference on Micro- and Nanosystems; and 9th International Conference on Advanced Vehicle Tire Technologies, Parts A and B, 2007
MEMS parallel-plate tunable capacitors are widely used in different areas such as tunable filters... more MEMS parallel-plate tunable capacitors are widely used in different areas such as tunable filters, resonators and communications (RF) systems for their simple structures, high Q-factors and small sizes. However, these capacitors have relatively low tuning range (50%) and are subjected to highly sensitive and nonlinear capacitance-voltage (C-V) responses. In this paper novel designs are developed which have C-V responses with high linearity and tunability and low sensitivity. The designs use the flexibility of the moving plates. The plate is segmented to provide a controllable flexibility. Segments are connected together at end nodes by torsional springs. Under each node there is a step which limits the vertical movement of that node. An optimization program finds the best set of step heights that provides the highest linearity. Two numerical examples of three-segmented- and six-segmented-plate capacitors verify that the segmentation of moving plate can considerably improve the linea...
48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 2007
A frequency-dependent, Dynamic Finite Element (DFE) formulation is developed to study the coupled... more A frequency-dependent, Dynamic Finite Element (DFE) formulation is developed to study the coupled flexural–torsional vibration of a preloaded, linearly elastic, slender beam subjected to an axial load and end moment. Euler-Bernoulli bending and St. Venant torsion beam theories are used to develop the governing equations and the DFE solution. A nonlinear Eigenvalue problem is formulated and the Eigensolutions are determined using a dedicated Matlab ® code. The DFE frequency results, for an illustrative example, are validated against conventional Finite Element Method (FEM). Various classical boundary conditions and loadings are considered. As expected, tensile forces increase natural frequencies indicating beam stiffening, compared to compressive forces that reduce the beams stiffness, seen by a reduction in natural frequency. When a force and an end moment are acting in combination, the moment reduces the stiffness of the beam. Nevertheless, the stiffness of the beam is found to be ...
Volume 4: 20th International Conference on Design Theory and Methodology; Second International Conference on Micro- and Nanosystems, 2008
In conventional MEMS parallel-plate capacitor designs, the moving electrode is commonly modeled a... more In conventional MEMS parallel-plate capacitor designs, the moving electrode is commonly modeled as a rigid plate with flexible boundary conditions provided by a set of supporting beams. Such a capacitor generates limited tuning ratio up to 1.5 and its capacitance-voltage response is nonlinear. This paper presents novel designs where the moving electrodes are fixed-edge flexible plates. The plate displacement is selectively limited by a set of rigid steps, located between two electrodes, to generate a smooth and linear response and high tunability. Three different step heights are considered in the design and the linearity of the C-V curve is maximized by modifying the geometry of the plate, and changing the location and order of steps. Since the analytical solution for coupled electrostatic-structural physics in this case does not exist, ANSYS® FEM simulation is performed to obtain the C-V curves and optimize the design. Two designs with different electrode shapes, rectangular and c...