Analytical approximations to nonlinear vibration of an electrostatically actuated microbeam

Qian, Youhua; Ren, Dongxu; Lai, Shih-Kung; Chen, S.M.

doi:10.1016/j.cnsns.2011.09.018

Cited by 39 publications

(18 citation statements)

References 21 publications

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“…Nathanson et al (1967) and Taylor (1968) had an experimental study on the pull-in instability of electrostatically-actuated micro electromechanical systems (MEMS). Qian et al (2012) the large-amplitude vibration of electrostatically actuated microbeams by using an homotopy analysis method. They used the Euler-Bernoulli beam theory and the Galerkin approach for the MEMS beam model.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear vibration of an electrostatically actuated microbeam

Bayat¹

2014

Lat. Am. j. solids struct.

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In this paper, we have considered a new class of critical technique that called the He's Variational Approach (VA) to solve the nonlinear vibration of an electrostatically actuated microbeam. It has been indicated that the Variational Approach (VA) is quickly convergence and does not demand small perturbation and also sufficiently accurate to both linear and nonlinear problems in engineering. The obtained results show that the approximate solutions are uniformly legitimate on the whole solution field.

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Section: Introductionmentioning

confidence: 99%

Nonlinear vibration of an electrostatically actuated microbeam

Bayat¹

2014

Lat. Am. j. solids struct.

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“…Alguns, recentes resultados na literatura, tem mostrado que, quando o problemaé modelado com condições de contorno do tipo Dirichlet ou Newman, o sistema apresenta comportamento oscilatório com presença de ruído, veja [1,3,[8][9][10][11].…”

Section: Metodologiaunclassified

Análise Numérica de Estabilidade de Estruturas Sujeitas a Condições de Fronteira Não Linear

Rabelo¹,

Gonçalves²,

Martinez³

et al. 2020

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

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“…[10] study free vibrations of tapered beams and give an accurate analytical solution for the thirdorder Duffing equations; Qian et al [11] obtain accurate analytical solutions for the fifth-order Duffing equations by considering vibrations of a restrained cantilever beam. For the seventh-order Duffing equations Qian et al [12] get accurate analytical solutions by researching vibrations of an electrostatically actuated microbeam.…”

Section: Introductionmentioning

confidence: 99%

Homotopy Analysis Method for Large-Amplitude Free Vibrations of Strongly Nonlinear Generalized Duffing Oscillators

Qian¹,

Ren²,

Chen³

et al. 2012

MME

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In this study, the homotopy analysis method (HAM) is used to solve the generalized Duffing equation. Both the frequencies and periodic solutions of the nonlinear Duffing equation can be explicitly and analytically formulated. Accuracy and validity of the proposed techniques are then verified by comparing the numerical results obtained based on the HAM and numerical integration method. Numerical simulations are extended for even very strong nonlinearities and very good correlations which achieved between the results. Besides, the optimal HAM approach is introduced to accelerate the convergence of solutions

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Analytical approximations to nonlinear vibration of an electrostatically actuated microbeam

Cited by 39 publications

References 21 publications

Nonlinear vibration of an electrostatically actuated microbeam

Nonlinear vibration of an electrostatically actuated microbeam

Análise Numérica de Estabilidade de Estruturas Sujeitas a Condições de Fronteira Não Linear

Homotopy Analysis Method for Large-Amplitude Free Vibrations of Strongly Nonlinear Generalized Duffing Oscillators

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