Nonlinear Forced Vibration of Piezoelectric and Electrostatically Actuated Nano/Micro Piezoelectric Beam

  • Sayyid H. Hashemi Kachapi Department of Mechanical Engineering, Babol Noshirvani University of Technology
  • S.GH. Hashemi Kachapi


In this study, the nonlinear vibration analysis of nano/micro electromechanical (NEMS/MEMS) piezoelectric beam exposed to simultaneous electrostatic and piezoelectric actuation. NEMS/MEMS beam actuate with combined DC and AC electrostatic actuation on the through two upper and lower electrodes. An axial force proportional to the applied DC voltage is produced by piezoelectric layers present via a DC electric voltage applied in the direction of the height of the piezoelectric layers. The governing differential equation of the motion is derived using Hamiltonian principle based on the Eulere-Bernoilli hypothesis and then this partial differential equation (PDE) problem is simplified into an ordinary differential equation (ODE) problem by using the Galerkin approach. Hamiltonian approach has been used to solve the problem and introduce a design strategy. Phase plane diagram of piezoelectric and electrostatically actuated beam has plotted to show the stability of presented nonlinear system and natural frequencies are calculated to use for resonator design. The result compare with the numerical results (fourth-order Runge-Kutta method), and approximate is more acceptable and results show that one could obtain a predesign strategy by prediction of effects of mechanical properties and electrical coefficients on the stability and forced vibration of common electrostatically actuated micro beam.


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Author Biographies

Sayyid H. Hashemi Kachapi, Department of Mechanical Engineering, Babol Noshirvani University of Technology

 Department of Mechanical Engineering, Babol Noshirvani University of Technology, Babol, Iran

S.GH. Hashemi Kachapi

Department of Physics, Mazandaran University, Babolsar, Iran


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How to Cite
Hashemi Kachapi, S. H., & Hashemi Kachapi, S. (2019). Nonlinear Forced Vibration of Piezoelectric and Electrostatically Actuated Nano/Micro Piezoelectric Beam. MathLAB Journal, 3, 160-177. Retrieved from
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