Microsystem Technologies

, Volume 23, Issue 6, pp 1913–1926 | Cite as

Nonlinear dynamics of MEMS/NEMS resonators: analytical solution by the homotopy analysis method

  • Farid Tajaddodianfar
  • Mohammad Reza Hairi Yazdi
  • Hossein Nejat Pishkenari
Technical Paper


Due to various sources of nonlinearities, micro/nano-electro-mechanical-system (MEMS/NEMS) resonators present highly nonlinear behaviors including softening- or hardening-type frequency responses, bistability, chaos, etc. The general Duffing equation with quadratic and cubic nonlinearities serves as a characterizing model for a wide class of MEMS/NEMS resonators as well as lots of other engineering and physical systems. In this paper, after brief reviewing of various sources of nonlinearities in micro/nano-resonators and discussing how they contribute to the Duffing-type nonlinearities, we propose a Homotopy Analysis Method (HAM) approach for derivation of analytical solutions for the frequency response of the resonators. Toward this aim, we first apply the HAM to the proposed Duffing equation, and through this procedure, we derive the first-order and second-order HAM-based analytical solutions for the frequency response of the resonator. As the main novelty, we show that the second-order solution benefits from a tunable parameter, known as the convergence-control parameter, which is a distinguishing aspect of the HAM and plays a key role in enhancing the accuracy of the obtained analytical expressions in strongly nonlinear problems. We use the obtained analytical solutions for the study of nonlinear dynamics in two types of electrostatically actuated MEMS resonators proposing hardening, softening or mixed behaviors near their primary resonance frequency. Numerical simulations are performed to validate the analytical results.


Frequency Response Homotopy Analysis Method Analytical Frequency Response Squeeze Film Multiple Scale Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The authors would like to gratefully thank the Iran National Science Foundation (INSF) for their financial support.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Farid Tajaddodianfar
    • 1
  • Mohammad Reza Hairi Yazdi
    • 1
  • Hossein Nejat Pishkenari
    • 2
  1. 1.School of Mechanical Engineering, College of EngineeringUniversity of TehranTehranIran
  2. 2.Nano Robotics Laboratory, School of Mechanical EngineeringSharif University of TechnologyTehranIran

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