Parametrically excited nonlinear dynamic instability of reinforced piezoelectric nanoplates

摘要

The nonlinear dynamic instability of reinforced piezoelectric nanoplates exposed to a parametric excitation and an electric voltage is the objective of the present paper. Firstly, a piezoelectric nanoplate reinforced with two graphene layers and resting on a visco-elastic foundation is modeled. Secondly, the piezoelectric nonlocal elasticity theory, the Kelvin-Voigt model, von Karman nonlinear relations and Hamilton's principle, respectively, are used to derive the nonlinear governing differential equation of motion. In the next step, to transform partial differential equation to ordinary one and then, solve the equation, the Galerkin technique and multiple time scales method are employed respectively. At the end, the modulation equation of reinforced piezoelectric nanoplates is obtained. Emphasizing the effect of the electric voltage and parametric excitation on dynamic instability of the system, trivial and nontrivial steady-state solutions are discussed. The main results emphasize that the damping coefficient is responsible of the bifurcation point variation, while the amplitude response depends on the term of natural frequency. Therefore, damping can have a strong influence on the system.