Vibrational analysis of electrostatically actuated microstructures considering nonlinear effects

Zand, Mahdi Moghimi; Ahmadian, Mohammad Taghi

doi:10.1016/j.cnsns.2008.05.009

Cited by 61 publications

(20 citation statements)

References 11 publications

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“…Micro-and nanoscale beams are increasingly used in micro-and nanoelectromechanical systems such as vibration shock sensors [Lun et al 2006], electrostatically excited microactuators [Moghimi Zand and Ahmadian 2009;Mojahedi et al 2010], microswitches [Coutu et al 2004], and atomic force microscopes [Mahdavi et al 2008]. The thickness of microscale beams is on the order of microns and submicrons.…”

Section: Introductionmentioning

confidence: 99%

A nonlinear Timoshenko beam formulation based on strain gradient theory

Ansari

Gholami

Darabi

2012

J. Mech. Mater. Struct.

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Developed herein is a comprehensive geometrically nonlinear size-dependent microscale Timoshenko beam model based on strain gradient and von Kármán theories. The nonlinear governing equations and the corresponding boundary conditions are derived from employing Hamilton's principle. A simply supported microbeam is considered to delineate the nonlinear size-dependent free vibration behavior of the presented model. Utilizing the harmonic balance method, the solution for free vibration is presented analytically. The influence of the geometric parameters, Poisson's ratio, and material length-scale parameters on the linear frequency and nonlinear frequency ratio are thoroughly investigated. The results obtained from the present model are compared, in special cases, with those of the linear strain gradient theory, linear and nonlinear modified couple stress theory, and linear and nonlinear classical models; excellent agreement is found. It is concluded that the nonlinear natural frequency and nonlinear frequency ratio predicted by strain gradient theory are more precise than those from the other theories mentioned, especially for shorter beams.

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Section: Introductionmentioning

confidence: 99%

A nonlinear Timoshenko beam formulation based on strain gradient theory

Ansari

Gholami

Darabi

2012

J. Mech. Mater. Struct.

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“…Younis [19] studied e ects of squeezelm damping, thermoelastic damping, and structural forces in an electrostatically actuated MEMS system and, to do so, he utilized a hybrid numerical-analytical solution. Moghimi Zand and Ahmadian [20] studied dynamic behavior of an electrostatically actuated microbeam while considering in-plane forces. They used First-order Shear Deformation Theory (FSDT) and applied Hybrid FEM-FDM to solve plate equations and Reynolds equation of squeeze lm damping, simultaneously.…”

Section: Introductionmentioning

confidence: 99%

Transient behavior of electrostatically-actuated micro systems considering squeeze film damping and mechanical shock

Abderezaei

Zand

2017

Scientia Iranica

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Abstract. In this paper, the dynamics of microbeams under the e ects of electrostatic force, mechanical shock, Squeeze Film Damping (SQFD), and fringing eld are modeled. A Galerkin-based reduced-order model is used to convert the Partial Di erential Equation of motion (PDE) to an Ordinary Di erential Equation (ODE). Furthermore, the system dynamics are studied using the developed nonlinear nite element code. Two di erent simpler models are validated by the results in the literature, which are in good compatibility with them. It is shown that the e ect of squeeze lm damping can dominate mechanical shock signi cantly. The response of microbeam to electrostatic actuation is also delayed when damping is included. The simultaneous and sole e ects of electrostatic actuation, mechanical shock, squeeze lm damping, and fringing eld are investigated in this study for the rst time.

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“…In [1], vibrations of double-clamped microbeams, under an electric eld, have been investigated. Vibrations of electrostatically actuated microstructures have also been studied in [8][9][10].…”

Section: Introductionmentioning

confidence: 99%

“…Di erent techniques have been proposed for nding solutions to nonlinear equations of MEMS: the di erential quadrature method [25], the nite-element method [9,10], and homotopy methods [26]. Although it is di cult to get an analytic approximation for di erent phenomena in MEMS, there are some analytic methods for nonlinear problems of microelectromechanical systems such as perturbation techniques [27,28].…”

Section: Introductionmentioning

confidence: 99%

Pull-in criteria of a nonclassical microbeam under electric field using homotopy method

2017

Self Cite

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Abstract. In this study, a homotopy analysis method was used to obtain analytic solutions to predict dynamic pull-in instability of an electrostatically-actuated microbeam. The nonlinear describing equation of a microbeam a ected by an electric eld, including the fringing eld e ect, was obtained based on strain gradient elasticity, couple stress, and classical theory. In uences of di erent parameters on dynamic pull-in instability were investigated. The equation of motion of a double-clamped microbeam was discretized and solved by using Galerkin's method via mode summation. The resulting non-linear di erential equation was also solved by using the Homotopy Analysis Method (HAM). The in uence of HAM parameters on accuracy was studied speci cally in the vicinity of the pull-in voltage. Comparison of the results of pull-in voltage indicated that low-voltage good agreement exists between numerical and semi-analytical methods, while HAM results deviated from those of numerical methods at high voltages. Findings indicate that strain gradient and couple stress e ects result in a sti er microbeam than with classical theory. E ects of an auxiliary parameter on convergence were also studied. Convergence domains were determined at di erent voltages and orders of HAM approximation.

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Vibrational analysis of electrostatically actuated microstructures considering nonlinear effects

Cited by 61 publications

References 11 publications

A nonlinear Timoshenko beam formulation based on strain gradient theory

A nonlinear Timoshenko beam formulation based on strain gradient theory

Transient behavior of electrostatically-actuated micro systems considering squeeze film damping and mechanical shock

Pull-in criteria of a nonclassical microbeam under electric field using homotopy method

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