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Homotopy Analysis Method for Nonlinear Dynamical System of an Electrostatically Actuated Microcantilever

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  • Y. M. Chen
  • G. Meng
  • J. K. Liu
  • J. P. Jing

Abstract

The homotopy analysis method (HAM) is employed to propose an approach for solving the nonlinear dynamical system of an electrostatically actuated micro-cantilever in MEMS. There are two relative merits of the presented HAM compared with some usual procedures of the HAM. First, a new auxiliary linear operator is constructed. This operator makes it unnecessary to eliminate any secular terms. Furthermore, all the deformation equations are purely linear. Numerical examples show the excellent agreement of the attained solutions with numerical ones. The respective effects of applied voltage, cubic nonlinear stiffness, gap distance, and squeeze film damping on vibration responses are analyzed detailedly.

Suggested Citation

  • Y. M. Chen & G. Meng & J. K. Liu & J. P. Jing, 2011. "Homotopy Analysis Method for Nonlinear Dynamical System of an Electrostatically Actuated Microcantilever," Mathematical Problems in Engineering, Hindawi, vol. 2011, pages 1-14, January.
    • Handle: RePEc:hin:jnlmpe:173459
    DOI: 10.1155/2011/173459
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    Cited by:

    1. Roy, Tapas & Maiti, Dilip K., 2024. "General approach on the best fitted linear operator and basis function for homotopy methods and application to strongly nonlinear oscillators," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 44-64.

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