Investigation of flexoelectric effect on nonlinear forced vibration of piezoelectric/functionally graded porous nanocomposite resting on viscoelastic foundation

Abstract

Investigation of flexoelectric effect on nonlinear forced vibration of piezoelectric/functionally graded porous nanocomposite is the objective of this study. The nanocomposite is exposed to electric voltage and external parametric excitation. First, a functionally graded porous core nanoplate is modeled and then two piezoelectric layers are glued with core. It is also rested on a visco-Pasternak foundation. Second, to derive governing equation of motion, two theories including Mindlin and Kirchhoff plate theories and Hamilton’s principle are utilized. In the next step, to obtain and solve ordinary differential equation, Galerkin technique and multiple time scales method are used, respectively. At the end, modulation equation of piezoelectric/functionally graded porous nanocomposite for both primary and secondary resonances is obtained and discussed. Emphasizing the effect of piezoelectric and flexoelectric, von Karman nonlinear deformation and parametric external excitation are simultaneously taken into account. It is found that electric voltage has no effect on the performance of piezoelectricity and flexoelectricity of the material on vibration behavior. The results of this study can be useful as benchmark for the next investigations in field of energy harvesting systems and piezoelectric structures.