Acta Mechanica Sinica

, Volume 35, Issue 1, pp 129–143 | Cite as

Nonlinear vibration analysis of a circular micro-plate in two-sided NEMS/MEMS capacitive system by using harmonic balance method

  • Milad SaadatmandEmail author
  • Alireza Shooshtari
Research Paper


In this study, forced nonlinear vibration of a circular micro-plate under two-sided electrostatic, two-sided Casimir and external harmonic forces is investigated analytically. For this purpose, at first, von Kármán plate theory including geometrical nonlinearity is used to obtain the deflection of the micro-plate. Galerkin decomposition method is then employed, and nonlinear ordinary differential equations (ODEs) of motion are determined. A harmonic balance method (HBM) is applied to equations and analytical relation for nonlinear frequency response (F–R) curves are derived for two categories (including and neglecting Casimir force) separately. The analytical results for three cases: (1) semi-linear vibration; (2) weakly nonlinear vibration; (3) highly nonlinear vibration, are validated by comparing with the numerical solutions. After validation, the effects of the voltage and Casimir force on the natural frequency of two-sided capacitor system are investigated. It is shown that by assuming Casimir force in small gap distances, reduction of the natural frequency is considerable. The influences of the applied voltage, damping, micro-plate thickness and Casimir force on the frequency response curves have been presented too. The results of this study can be useful for modeling circular parallel-plates in nano/microelectromechanical transducers such as microphones and pressure sensors.


Nonlinear vibration Two-sided MEMS capacitor Circular plate Harmonic balance method 



We are deeply grateful to Prof. Jakob Søndergaard Jensen, who is chief of the Center for Acoustic-Mechanical Micro Systems (CAMM) in Technical University of Denmark (DTU), for his kind guidance and revisions that enriched the contents of this manuscript.


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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Electrical EngineeringTechnical University of DenmarkKgs. LyngbyDenmark
  2. 2.Department of Mechanical EngineeringBu-Ali Sina UniversityHamedanIran

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