Resonance analysis on nonlinear vibration of piezoelectric/FG porous nanocomposite subjected to moving load

Since micro/nano-electromechanical devices made of nanocomposites are strongly influenced by external excitations, this paper intends to comprehensively investigate the effect of the primary and secondary resonances in performance of nano-electromechanical systems (NEMS). This model also helps to analyze nonlinear vibration behaviors of the recently built single-layered graphene sheet (SLGS) and multi-layered graphene sheet (MLGS) nanomechanical resonators. The aim of this work is to derive the effect of primary and secondary resonances in nonlinear forced vibration of piezoelectric/functionally graded (FG) porous nanocomposite subjected to a moving load and external electric voltage. At first, an FG porous core nanoplate glued with two piezoelectric layers is modeled. Then, the modeled nanocomposite is rested on a visco-Pasternak foundation. In the next step, Mindlin and Kirchhoff plate theories and Hamilton's principle are separately employed to derive governing equation of motion. Galerkin technique and multiple time scales method are used, respectively, to solve the equation. Furthermore, primary and secondary resonances are analyzed and modulation equation of piezoelectric/FG porous nanocomposite for both of them is obtained. Finally, modulation equation under sub-harmonic and super-harmonic stimulations is studied and graphs are derived. Results show that there is a periodic relation between amplitude response and velocity of moving load. Also, even in the absence of electric voltage, the piezoelectric effect of the material can reduce the nonlinear vibration.