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Journal of Applied Nonlinear Dynamics 9(2) (2020) 307--321 | DOI:10.5890/JAND.2020.06.011

Sayyid H. Hashemi Kachapi$^{1}$, S. GH. Hashemi Kachapi$^{2}$

$^{1}$ Department of Mechanical Engineering, Babol Noshirvani University of Technology, Babol, Iran

$^{2}$ Department of Physics, Mazandaran University, Babolsar, Iran

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Abstract

In this work, nonlinear dynamics and parametric excitation of piezoelectric micro beam subjected a combination of DC and AC voltages is investigated for micro biological sensor applications. The governing differential equation of the motion is derived by the Hamiltonian principle and then by using the Galerkin approach, this partial differential equation (PDE) is simplified into an ordinary differential equation (ODE) in terms of forced damped Mathieu equation with cubic nonlinearity. A perturbation technique, i.e. multiple time scales approach is used for investigation of superharmonic resonances of orders 1/2 and 1/3 and obtaining of the modulation equations in the amplitude and phase. Numerical results of different parameters effects on the piezoelectric micro beam behavior are presented graphically.

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