Static pull-in analysis of electrostatically actuated microbeams using homotopy perturbation method

Mojahedi, Mahdi; Zand, Mahdi Moghimi; Ahmadian, Mohammad Taghi

doi:10.1016/j.apm.2009.07.013

Cited by 112 publications

(33 citation statements)

References 22 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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“…Due to the importance and wide application of microbeam-based microstructures, many analytical/numerical analyses from various viewpoints, considering various configurations of the microbeam with different load types, were performed, and applicable results were extracted. For example, the static deflection and instability of the nonlinear micro/nano cantilever beam with tip mass was studied by Mojahedi et al (2010). Using a homotopy perturbation method, they investigated the effects of van der Waals and Casimir forces on the static deflection and pull-in instability of the system.…”

Section: Introductionmentioning

confidence: 99%

Vibration behavior of a viscoelastic composite microbeam under simultaneous electrostatic and piezoelectric actuation

Yazdi

Jalali

2015

Mech Time-Depend Mater

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In this paper, the static and dynamic response of a clamped-clamped viscoelastic nanocomposite microbeam under combined electrostatic and piezoelectric actuations is analyzed. The equations of motion of the system are derived using the Euler-Bernoulli beam theory, Kelvin-Voigt model and Hamilton principle. The nonlinear model for the system is studied by considering stretching of the mid-plane, a DC electrostatic force, an AC harmonic force and a DC piezoelectric actuation. The static deflection and natural frequency of the system is extracted, and the influence of system parameters on the primary resonance behavior of the system is studied. It is shown that, based on various electrostatic and piezoelectric excitations, hardening or softening behavior is expected. So, one can tune these voltages such that this highly nonlinear system behaves linearly close to resonance frequency. Also it is shown that damping characteristics of the system with viscoelastic material not only depends on the damping coefficient of the system, but also on its other parameters.

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“…The effects of geometric parameters such as beam lengths, width, thickness, gaps, and size effect are discussed in detail through a numerical study. Mojahedi et al [14] studied static pull-in instability of electrostatically-actuated microbridges and microcantilevers considering different nonlinear effects. The nonlinear differential equations are converted by means of Galerkin's decomposition method into nonlinear integro-differential equations.…”

Section: Introductionmentioning

confidence: 99%

Optimal homotopy asymptotic method to large post-buckling deformation of MEMS

Herişanu

Marinca

2018

MATEC Web Conf.

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Abstract. In the present paper, the post-buckling response of an axially stressed clampedclamped actuator, modeled as a beam and subjected to a symmetric electrostatic field is analyzed. An analytical approximate method, namely the Optimal Homotopy Asymptotic Method (OHAM) is applied to the governing nonlinear integro-differential equation. The analytical results obtained through the proposed procedure show excellent agreement with numerical solution, proving the validity of the proposed procedure, which is simple and easy to use.

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Static pull-in analysis of electrostatically actuated microbeams using homotopy perturbation method

Cited by 112 publications

References 22 publications

A nonlinear Timoshenko beam formulation based on strain gradient theory

A nonlinear Timoshenko beam formulation based on strain gradient theory

Vibration behavior of a viscoelastic composite microbeam under simultaneous electrostatic and piezoelectric actuation

Optimal homotopy asymptotic method to large post-buckling deformation of MEMS

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