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Closed form solutions for electrostatically actuated micromirrors considering the bending effect
, Article ASME 2011 International Mechanical Engineering Congress and Exposition, IMECE 2011 ; Volume 11 , 2011 , Pages 897-902 ; 9780791854976 (ISBN) ; Ahmadian, M. T ; Moeenfard, H ; Sharif University of Technology
2011
Abstract
In the current paper, analytical solutions are presented for the nonlinear problem of electrostatically actuated torsional micromirrors considering the bending of the torsional beams. Energy method is used for finding the equilibrium equations. Then the explicit function theorem is utilized for finding the equations governing the instability mode of the mirror. The presented results show that neglecting the bending effect in electrostatic torsion micro actuators can cause to several hundred percent of overestimation of the stability limits of the device. In order to study the voltage-angle and voltage-displacement behavior of the micromirror, equilibrium equations are solved using HPM....
Free vibration analysis of a nonlinear beam using homotopy and modified lindstedt-poincare methods
, Article Journal of Solid Mechanics ; Volume 1, Issue 1 , Volume 1, Issue 1 , 2009 , Pages 29-36 ; 20083505 (ISSN) ; Mojahedi, M ; Moeenfard, H ; Sharif University of Technology
2009
Abstract
In this paper, homotopy perturbation and modified Lindstedt-Poincare methods are employed for nonlinear free vibrational analysis of simply supported and double-clamped beams subjected to axial loads. Mid-plane stretching effect has also been accounted in the model. Galerkin's decomposition technique is implemented to convert the dimensionless equation of the motion to nonlinear ordinary differential equation. Homotopy and modified Lindstedt-Poincare (HPM) are applied to find analytic expressions for nonlinear natural frequencies of the beams. Effects of design parameters such as axial load and slenderness ratio are investigated. The analytic expressions are valid for a wide range of...
Application of the extended kantorovich method to the static deflection of microplates under capillary force
, Article ASME International Mechanical Engineering Congress and Exposition, Proceedings (IMECE), 12 November 2010 through 18 November 2010 ; Volume 10 , November , 2010 , Pages 113-119 ; 9780791844472 (ISBN) ; Kahrobaiyan, M. H ; Ahmadian, M. T ; Sharif University of Technology
2010
Abstract
The aim of this paper is to apply an Extended Kantorovich method (EKM) to simulate the static deflection of microplates under capillary force. The model accounts for the capillary force nonlinearity of the excitation. Starting from a one term Galerkin approximation and following the Extended Kantorovich procedure, the equations governing the microplate deflection are obtained. These equations are then solved iteratively with a rapid convergence procedure to yield the desired solution. The effects of capillary force on the pull-in phenomenon of microplates are delineated in some figures. It is shown that rapid convergence, high precision and independency of initial guess function makes the...
Nonlinear dynamic modeling of surface defects in rolling element bearing systems
, Article Journal of Sound and Vibration ; Volume 319, Issue 3-5 , 2009 , Pages 1150-1174 ; 0022460X (ISSN) ; Abbasion, S ; Farshidianfar, A ; Moeenfard, H ; Sharif University of Technology
2009
Abstract
In this paper an analytical model is proposed to study the nonlinear dynamic behavior of rolling element bearing systems including surface defects. Various surface defects due to local imperfections on raceways and rolling elements are introduced to the proposed model. The contact force of each rolling element described according to nonlinear Hertzian contact deformation and the effect of internal radial clearance has been taken into account. Mathematical expressions were derived for inner race, outer race and rolling element local defects. To overcome the strong nonlinearity of the governing equations of motion, a modified Newmark time integration technique was used to solve the equations...
An analytical approach to modeling static behavior of torsional nano-/micro-actuators under effect of van der Waals force
, Article Japanese Journal of Applied Physics ; Volume 51, Issue 3 PART 1 , 2012 ; 00214922 (ISSN) ; Darvishian, A ; Ahmaidan, M. T ; Zohoor, H ; Sharif University of Technology
2012
Abstract
In this research, the static behavior of torsional nano-/micro-actuators under van der Waals (vdW) force is studied. First, the equilibrium equation governing the static behavior of torsional nano-/micro-actuators under vdW force is obtained. Then the energy method is utilized to investigate the statical stability of nano-/micro-actuator equilibrium points and a useful equation is suggested for the successful and stable design of nano-/micro-actuators under vdW force. Then, the equilibrium angle of nano-/micro-actuators is calculated both numerically and analytically using the homotopy perturbation method (HPM). It is observed that, with increasing instability number, defined in this paper,...
Influence of Van der Waals force on static behavior of nano/micromirrors under capillary force
, Article International Journal of Modern Physics B ; Volume 26, Issue 7 , 2012 ; 02179792 (ISSN) ; Darvishian, A ; Zohoor, H ; Ahmadian, M. T ; Sharif University of Technology
2012
Abstract
In the current paper, the effect of van der Waals (vdW) force on the static behavior and pull-in characteristics of nano/micromirrors under capillary force is investigated. At first, the dimensionless equation governing the static behavior of nano/micromirrors is obtained. The dependence of the critical tilting angle on the physical and geometrical parameters of the nano/micromirror and its supporting torsional beams is investigated. It is found that the existence of vdW force can considerably reduce the stability limits of the nano/micromirror. It is also found that rotation angle of the mirror due to capillary force highly depends on the vdW force applied to the mirror. Finally, analytical...
Characterization of the static behavior of micromirrors under the effect of capillary force, an analytical approach
, Article Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science ; Volume 226, Issue 9 , January , 2012 , Pages 2361-2372 ; 09544062 (ISSN) ; Darvishian, A ; Zohoor, H ; Ahmadian, M. T ; Sharif University of Technology
SAGE
2012
Abstract
In this article, the static behavior of micromirrors under the effect of capillary force is studied. The dimensionless equations governing the static behavior and the pull-in state of the micromirror under capillary force are obtained, and the effects of different geometrical parameters on the pull-in angle of micromirrors are investigated. The static behavior of micromirrors is studied both numerically and analytically using the homotopy perturbation method. It is observed that with increasing the instability number defined in this article, the rotation angle of the micromirror is increased and suddenly the pull-in occurs. The results of the presented model are then verified by comparing...
Modeling geometric non-linearities in the free vibration of a planar beam flexure with a tip mass
, Article Proceedings of the ASME Design Engineering Technical Conference, 12 August 2012 through 12 August 2012 ; Volume 4, Issue PARTS A AND B , August , 2012 , Pages 363-371 ; 9780791845035 (ISBN) ; Awtar, S ; Sharif University of Technology
2012
Abstract
The objective of this work is to create an analytical framework to study the non-linear dynamics of beam flexures with a tip mass undergoing large deflections. Hamilton's principal is utilized to derive the equations governing the nonlinear vibrations of the cantilever beam and the associated boundary conditions. Then, using a single mode approximation, these non-linear partial differential equations are reduced to two coupled non-linear ordinary differential equations. These equations are solved analytically using combination of the method of multiple time scales and homotopy perturbation analysis. Closed-form, parametric analytical expressions are presented for the time domain response of...
Analytical modeling of bending effect on the torsional response of electrostatically actuated micromirrors
, Article Optik ; Volume 124, Issue 12 , June , 2013 , Pages 1278-1286 ; 00304026 (ISSN) ; Ahmadian, M. T ; Sharif University of Technology
2013
Abstract
This paper presents analytical soltions for the nonlinear problem of electrostatically actuated torsional micromirrors considering the bending of the torsional beams. First the energy method is used for finding the equilibrium equations. Then the explicit function theorem is utilized for finding the equations governing the instability mode of the mirror. These equations are then solved using Homotopy Perturbation Method (HPM) for the especial case of α = 0 where α is a small nondimensional geometrical parameter defining the starting point of the underneath electrodes. Then straight forward perturbation method is applied for finding the pull-in angle and pull-in displacement of the...
Analytical closed form model for static pull-in analysis in electrostatically actuated torsional micromirrors
, Article Journal of Mechanical Science and Technology ; Volume 27, Issue 5 , 2013 , Pages 1443-1449 ; 1738494X (ISSN) ; Ahmadian, M. T ; Sharif University of Technology
2013
Abstract
The objective of this work is to create an analytical framework to study the static pull-in and also equilibrium behavior in electrostatically actuated torsional micromirrors. First the equation governing the static behavior of electrostatic torsion micromirrors is derived and normalized. Perturbation method, the method of straight forward expansion is utilized to find the pull-in angle of the mirror. Comparison of the presented results with numerical ones available in the literature shows that the proposed second order perturbation expansion gives very precise approximations for the pull-in angle of the mirror. Then straightforward perturbation expansion method is used again to analytically...
The influence of vertical deflection of the supports in modeling squeeze film damping in torsional micromirrors
, Article Microelectronics Journal ; Volume 43, Issue 8 , 2012 , Pages 530-536 ; 00262692 (ISSN) ; Taghi Ahmadian, M ; Sharif University of Technology
Elsevier
2012
Abstract
The objective of this work is to create an analytical framework to study the problem of squeezed film damping in micromirrors considering the bending of the supporting torsion microbeams. Using mathematical and physical justifications, nonlinear Reynolds equation governing the behavior of the squeezed gas underneath the mirror is linearized. The resulting linearized equation is then nondimensionalized and analytically solved for two cases of the infinitesimal and finite tilting angle of the mirror. The obtained pressure distribution from the solution of the Reynolds equation is then utilized for finding the squeezed film damping force and torque applied to the mirror. The results show that...
Analytical modeling of static behavior of electrostatically actuated nano/micromirrors considering van der Waals forces
, Article Acta Mechanica Sinica/Lixue Xuebao ; Volume 28, Issue 3 , June , 2012 , Pages 729-736 ; 05677718 (ISSN) ; Ahmadian, M. T ; Sharif University of Technology
2012
Abstract
In this paper, the effect of van der Waals (vdW) force on the pull-in behavior of electrostatically actuated nano/micromirrors is investigated. First, the minimum potential energy principle is utilized to find the equation governing the static behavior of nano/micromirror under electrostatic and vdW forces. Then, the stability of static equilibrium points is analyzed using the energy method. It is found that when there exist two equilibrium points, the smaller one is stable and the larger one is unstable. The effects of different design parameters on the mirror's pull-in angle and pull-in voltage are studied and it is found that vdW force can considerably reduce the stability limit of the...
A coupled two degree of freedom model for nano/micromirrors under van der waals force
, Article Proceedings of the ASME Design Engineering Technical Conference ; Volume 5 , 2012 , Pages 145-150 ; 9780791845042 (ISBN) ; Darvishian, A ; Ahmadian, M. T ; Sharif University of Technology
2012
Abstract
The current paper presents a two degree of freedom model for the problem of nano/micromirrors under the effect of vdW force. Energy method, the principal of minimum potential energy is employed for finding the equilibrium equations governing the deflection and the rotation of the nano/micromirror. Then using the implicit function theorem, a coupled bending-torsion model is presented for the pull-in characteristics of nano/micromirrors under vdW force and the concept of instability mode is introduced. It is observed that with increasing the ratio of the bending stiffness to the torsion stiffness, the dominant instability mode changes from bending mode to the torsion mode. It is shown that...
Coupled bending and torsion effects on the squeezed film air damping in torsional micromirrors
, Article Proceedings of the ASME Design Engineering Technical Conference, 12 August 2012 through 12 August 2012 ; Volume 5 , August , 2012 , Pages 49-55 ; 9780791845042 (ISBN) ; Kaji, F ; Ahmadi, M. T ; Sharif University of Technology
2012
Abstract
The current paper presents an analytical model for the problem of squeezed film damping in micromirrors considering the bending of the supporting torsion microbeams. At the first the nonlinear Reynolds equation governing the behavior of the squeezed gas underneath the mirror is linearized. The resulting linearized equation is then nondimensionalized and analytically solved for two cases of the infinitesimal and finite tiling angle of the mirror. The obtained pressure distribution from the solution of the Reynolds equation is then utilized for finding the squeezed film damping force and torque applied to the mirror. The results show that in the case of the infinitesimal tilting angle, the...
A coupled bending-torsion model for electrostatically actuated torsional nano/micro-actuators with considering influence of van der Waals force
, Article Acta Mechanica ; Volume 224, Issue 8 , 2013 , Pages 1791-1800 ; 00015970 (ISSN) ; Darvishian, A ; Ahmadian, M. T ; Sharif University of Technology
2013
Abstract
In the current paper, a coupled two degree of freedom model which considers both bending and torsion of the supporting torsion beams is presented for electrostatically actuated torsional nano/micro-actuators under the effect of van der Waals (vdW) force. Newton's second law is utilized for finding the normalized equations governing the static behavior of the actuator. The implict function theorem is then utilized for finding the equations governing the pull-in state of the actuator. The related results show that torsion model considerably overestimates the pull-in parameters of the nano/micro-actuator. The concept of the instability mode is introduced, and it is shown that when the ratio of...
Static behavior of nano/micromirrors under the effect of Casimir force, an analytical approach
, Article Journal of Mechanical Science and Technology ; Volume 26, Issue 2 , FEB , 2012 , Pages 537-543 ; 1738494X (ISSN) ; Darvishian, A ; Ahmaidan, M. T ; Sharif University of Technology
2012
Abstract
In this paper, static behavior of nano/microm1irrors under Casimir force is studied. At the first, the equilibrium equation governing the statical behavior of nano/micromirrors is obtained. Then energy method is employed to investigate statical stability of nano/micromirrors equilibrium points and a useful equation is suggested for successful and stable design of nano/micromirrors under Casimir force. Then, equilibrium angle of nano/micromirrors is calculated both numerically and analytically using the homotopy perturbation method (HPM). It is observed that with increasing the instability number defined in the paper, the rotation angle of the mirror is increased and suddenly, pull-in occurs....
A homotopy perturbation analysis of nonlinear free vibration of Timoshenko microbeams
, Article Journal of Mechanical Science and Technology ; Volume 25, Issue 3 , 2011 , Pages 557-565 ; 1738494X (ISSN) ; Mojahedi, M ; Ahmadian, M. T ; Sharif University of Technology
2011
Abstract
This paper uses Hes Homotopy Perturbation Method (HPM) to analyze the nonlinear free vibrational behavior of clamped-clamped and clamped-free microbeams considering the effects of rotary inertia and shear deformation. Galerkins projection method is used to reduce the governing nonlinear partial differential equation. to a nonlinear ordinary differential equation. HPM is used to find analytic expressions for nonlinear natural frequencies of the pre-stretched microbeam. A parametric study investigated the effects of design parameters such as applied axial loads and slenderness ratio. The effect of rotary inertia and shear deformation on the nonlinear natural frequency was investigated. For...
Analytical modeling of the effects of electrostatic actuation and casimir force on the pull-in instability and static behavior of torsional nano/micro actuators
, Article International Journal of Modern Physics B ; Volume 27, Issue 6 , 2013 ; 02179792 (ISSN) ; Darvishian, A ; Ahmadian, M. T ; Sharif University of Technology
2013
Abstract
This paper studies the effect of Casimir force on the pull-in instability of electrostatically actuated torsional nano/micro actuators. Dependence of the actuator's pull-in angle and pull-in voltage on several design parameters are investigated and it is found that Casimir force can considerably reduce the stability limits of the torsional actuators. Nonlinear equilibrium equation is solved numerically and analytically using straight forward perturbation expansion method. It is observed that a fourth-order perturbation approximation can precisely model the behavior of a torsional actuator. The results of this paper can be used for safe and stable design of torsional nano/micro actuators
Modeling of Pull-In Instability of Nano/Micromirrors Under the Combined Effect of Capillary and Casimir Forces
, Article International Journal of Optomechatronics ; Volume 5, Issue 4 , Dec , 2011 , Pages 378-392 ; 15599612 (ISSN) ; Darvishian, A ; Ahmaidan, M. T ; Sharif University of Technology
2011
Abstract
In the current article the effect of the Casimir force on the static behavior and pull-in characteristics of nano/micromirrors under capillary force is investigated. At the first, the dimensionless equation governing the static behavior of nano/micromirrors is obtained. The dependency of the critical tilting angle on the physical and geometrical parameters of the nano/micromirror and its supporting torsional beams is investigated. It is found that the Casimir effect can considerably reduce the pull-in instability limits of the nano/micromirror. It is also found that rotation angle of the mirror under capillary force highly depends on the Casimir force applied to the mirror. Finally the...
Modeling squeezed film air damping in torsional micromirrors using extended Kantorovich method
, Article Meccanica ; Volume 48, Issue 4 , 2013 , Pages 791-805 ; 00256455 (ISSN) ; Ahmadian, M. T ; Farshidianfar, A ; Sharif University of Technology
2013
Abstract
The current paper uses the Extended Kantorovich Method (EKM) to analytically solve the problem of squeezed film damping in micromirrors. First a one term Galerkin approximation is used and following the extended Kantorovich procedure, the solution of the Reynolds equation which governs the squeezed film damping in micromirrors is reduced to solution of two uncoupled ordinary differential equation which can be solved iteratively with a rapid convergence for finding the pressure distribution underneath the micromirror. It is shown that the EKM results are independent of the initial guess function. It is also shown that EKM is highly convergent and practically one iterate is sufficient for...