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Meccanica
Published in: Meccanica 10/2017

30-11-2016

Investigation of size-dependent quasistatic response of electrically actuated nonlinear viscoelastic microcantilevers and microbridges

Author: Mohamed A. Attia

Published in: Meccanica | Issue 10/2017

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Abstract

This study investigates the size-dependent quasistatic response of a nonlinear viscoelastic microelectromechanical system (MEMS) under an electric actuation. To have this problem in view, the deformable electrode of the MEMS is modelled using cantilever and doubly-clamped viscoelastic microbeams. The modified couple stress theory in conjunction with Bernoulli–Euler beam theory are used for mathematical modeling of the size-dependent instability of microsystems in the framework of linear viscoelastic theory. Simultaneous effect of electrostatic actuation including fringing field, residual stress, mid-plane stretching and Casimir and van der Waals intermolecular forces are considered in the theoretical model. A single element of the standard linear solid element is used to simulate the viscoelastic behavior. Based on the extended Hamilton’s variational principle, the nonlinear governing integro-differential equation and boundary conditions are derived. Thereafter, a new generalized differential-integral quadrature solution for the nonlinear quasistatic response of electrically actuated viscoelastic micro/nanobeams under two different boundary conditions; doubly-clamped microbridge and clamped-free microcantilever. The developed model is verified and a good agreement is obtained. Finally, a comprehensive study is conducted to investigate the effects of various parameters such as material relaxation time, durable modulus, material length scale parameter, Casimir force, van der Waals force, initial gap and beam length on the pull-in response of viscoelastic microbridges and microcantilevers in the framework of viscoelasticity.
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Metadata
Title
Investigation of size-dependent quasistatic response of electrically actuated nonlinear viscoelastic microcantilevers and microbridges
Author
Mohamed A. Attia
Publication date
30-11-2016
Publisher
Springer Netherlands
Published in
Meccanica / Issue 10/2017
Print ISSN: 0025-6455
Electronic ISSN: 1572-9648
DOI
https://doi.org/10.1007/s11012-016-0595-8

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