Sayyid H. Hashemi Kachapi a, 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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