Sharif Digital Repository

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  

In this paper, a mathematical modeling of a microcantilever gyroscope is presented considering the nonlinearities of the system due to electrostatic forces, fringing field, geometry and the inertial terms. The microgyroscope is actuated and detected by electrostatic methods and subjected to coupled bending oscillations. First a system of two nonlinear integro-differential equations is derived which describes flexural-flexural motion of electrostatically actuated and detected microbeam gyroscopes. Afterward, static deflection and pull-in instability of the microgyroscopes acted upon by DC voltages in both (driving and sensing) directions are studied for different parameters. The model's... 

The coupling effect between torsion and bending in nano/micromirrors under the combined effect of capillary force and van der Waals (vdW) force is presented in this paper. At the first, the dimensionless equations governing the statical behavior of the nano/micromirror are obtained using the minimum total potential energy principle. Then the equations governing the pull-in state of the mirror are obtained using the implicit function theorem. The related results show that neglecting bending effect can lead to considerable overestimation in predicting the pull-in limits of the nano/micromirror under combined vdW and capillary forces. It is observed that vdW force reduces the pull-in angle and... 

In this study, homotopy analysis method is used to derive analytic solutions to predict dynamic pull-in instability of electrostatically-actuated microsystems. The model considers midplane stretching, initial stress, distributed electrostatic force and fringing fields effect. Influences of different parameters on dynamic pull-in instability are investigated. Results are in good agreement with numerical and experimental findings. © 2009 Elsevier Ltd. All rights reserved  

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... 

Based on the nonlocal Euler–Bernoulli beam theory, a theoretical approach is developed to investigate the effects of small scale and intermolecular force on the dynamic pull-in behavior of electrostatically actuated nanoresonators. To this purpose, nanoresonators are modeled as multilayer beams with rectangular cross-sections and fixed-fixed and fixed-free end conditions which are embedded in an elastic medium containing Winkler and Pasternak elastic foundations. Also, the effects of nonlocal parameter, fringing field due to the finite width of beams, Casimir or van der Waals intermolecular forces, nonlinear term induced by mid-plane stretching and Winkler and Pasternak elastic foundations... 

In this paper, vibration suppression of micro-or nano-scale beams subjected to nonlinear distributed electrostatic force is studied. For the sake of precision, we use the beam model derived from strain gradient elasticity theory aimed at prediction of size effect. In addition, the electrostatic force is considered with first order fringing field correction. The continuous model of the strain gradient beam is truncated by using Kantorovich method as a semi-analytical finite element method. A boundary control feedback law is proposed to suppress forced vibrations of the beam. Both measurements and actuations are taken place in the boundary to avoid spillover instabilities. Simulation results... 

The influence of Casimir and van der Waals forces on the instability of vibratory micro and nano-bridge gyroscopes with proof mass attached to its midpoint is studied. The gyroscope subjected to the base rotation, Casimir and van der Waals attractions is actuated and detected by electrostatic methods. The system has two coupled bending motions actuated by the electrostatic and Coriolis forces. First a system of nonlinear equations for the flexural-flexural deflection of beam gyroscopes is derived using the extended Hamilton's principle. In modeling, the nonlinearities due to mid-plane stretching, electrostatic forces, including fringing field, Casimir and van der Waals attractions, are... 

This paper deals with the study of the small scale effect on the pull-in instability of nano-switches subjected to electrostatic and intermolecular forces. Using Eringen's nonlocal elasticity theory, the nonlocal Euler-Bernoulli beam model is derived through virtual displacement principle. The static governing equation which is extremely nonlinear due to the intermolecular and electrostatic attraction forces is solved numerically by differential quadrature method. The accuracy of the present method is verified by comparing the obtained results with the finite difference method and those in the literatures and very good agreement is obtained. Finally a comprehensive study is carried out to... 

In this study, static pull-in instability of electrostatically-actuated microbridges and microcantilevers is investigated considering different nonlinear effects. Galerkin's decomposition method is utilized to convert the nonlinear differential equations of motion to nonlinear integro-algebraic equations. Afterward, analytic solutions to static deflections of the microbeams are obtained using the homotopy perturbation method. Results are in excellent agreement with those presented in the literature  

In this paper, the effects of van der Waals and Casimir forces on the static deflection and pull-in instability of a micro/nano cantilever gyroscope with proof mass at its end are investigated. The micro/nano gyroscope is subjected to coupled bending motions which are related by base rotation and nonlinearities due to the geometry and the inertial terms. It is actuated and detected by capacitance plates which are placed on the proof mass. The extended Hamilton principle is used to find the equations governing the static behavior of the clamp-free micro/nano gyroscopes under electrostatic, Casimir and van der Waals forces. The equations of static motion are discritized by Galerkin's... 

This paper analyzes the deflection and pull-in behaviors of cantilever and doubly clamped carbon nanotubes (CNTs) under electrostatic actuation using the homotopy perturbation method. The effects of electrostatic force and interatomic interactions on the deflection and pull-in instabilities of CNTs with different lengths, diameters, and boundary conditions are investigated in detail. The results reveal that larger diameters and shorter lengths result in higher pull-in voltages. Moreover, CNTs with doubly clamped boundary conditions, in comparison with cantilever boundary conditions, are more resistant to pull-in  

In this paper, a nonlinear model is used to analyze the dynamic pull-in instability and vibrational behavior of a microcantilever gyroscope. The gyroscope has a proof mass at its end and is subjected to nonlinear squeeze film damping, step DC voltages as well as base rotation excitation. The electrostatically actuated and detected microgyroscopes are subjected to coupled flexural-flexural vibrations that are related by base rotation. In order to detune the stiffness and natural frequencies of the system, DC voltages are applied to the proof mass electrodes in drive and sense directions. Nonlinear integro differential equations of the system are derived using extended Hamilton principle... 

Parallel micro actuators are mostly fabricated using the wet etching process within which the presence of capillary force and the resulting pull-in instabilities can severely affect the success of the fabrication process. In the case the capillary force is large enough then the beam like structure of the micro actuators is collapsed. The current paper investigates; static behavior of microcantilevers under effect of capillary force. It is observed that with increasing the instability number defined in the paper, the deflection of the micro-cantilevers is increased. This study shows in the wet etching fabrication process, if the distance between the beam and substrate is small enough, the... 

This paper presents the deflection and pull-in instability of the double-walled carbon nanotubes with different dimensions and boundary conditions. Molecular dynamic technique is applied to model the desired behaviors of the nano systems. The effects of cross-linking between the carbon walls are investigated on the pull-in charge. In addition, the influences of axial stretching on the pull-in charge and vibrational frequencies of the carbon nanotubes are scrutinized. The effects of electrostatic charge distribution on the vibration amplitude are also reported  

In this study, influences of intermolecular forces on dynamic pull-in instability of electrostatically actuated beams are investigated. Effects of midplane stretching, electrostatic actuation, fringing fields and intermolecular forces are considered. The boundary conditions of the beams are clamped-free and clamped-clamped. A finite element model is developed to discretize the governing equations and Newmark time discretization is then employed to solve the discretized equations. The results indicate that by increasing the Casimir and van der Waals effects, the effect of inertia on pull-in values considerably increases  

In this paper, modified Adomian decomposition (MAD) is introduced to investigate the effect of the Casimir attraction on pull-in instability of beam-type NEMS theoretically. Two engineering cases including cantilever and double cantilever nano-beam are considered. The proposed MAD method is employed to solve the nonlinear constitutive equation of nano-beams. The basic engineering parameters such as critical deflection and pull-in voltage of nano-beams are computed. It is found that the Casimir forces decrease the pull-in deflection and voltage of nano-beams. On the other hand, the fringing field increases the pull-in deflection while decreases the pull-in voltage of the actuators. As a... 

In this study, dynamic pull-in instability and snap-through buckling of initially curved microbeams are investigated. The microbeams are actuated by suddenly applied electrostatic force. A finite element model is developed to discretize the governing equations and Newmark time discretization is employed to solve the discretized equations. The static pull-in behavior is investigated to validate the model. The results of the finite element model are compared with finite difference solutions and their convergence is examined. In addition, the influence of different parameters on dynamic pull-in instability and snap-through buckling is explored  

For modeling the electromechanical behavior of nano-bridge structures with slender narrow-width beam elements, not only the simultaneous effects of surface layer and size dependency should be taken into account but also corrected force models should be considered. In this paper, the instability of a narrow-width nano-bridge is studied based on strain gradient theory and Gurtin–Murdoch surface elasticity. The mid-plane stretching is incorporated in the governing equation as well as corrected force distribution. Using Rayleigh–Ritz method, a parametric analysis is conducted to examine the impacts of surface layer, size dependence, dispersion forces and structural damping on static and dynamic... 

In this paper, a distributed parameter model is used to study the pull-in instability of cantilever type nanomechanical switches subjected to intermolecular and electrostatic forces. In modeling of the electrostatic force, the fringing field effect is taken into account. The model is nonlinear due to the inherent nonlinearity of the intermolecular and electrostatic forces. The nonlinear differential equation of the model is transformed into the integral form by using the Green's function of the cantilever beam. Closed-form solutions are obtained by assuming an appropriate shape function for the beam deflection to evaluate the integrals. The pull-in parameters of the switch are computed under...