Nonlinear forced vibration of thermo-electro-elastic piezoelectric-graphene composite nanoplate based on viscoelastic foundation

The dynamic behavior of a piezoelectric-graphene compound asymmetric nanoplate resting on a viscoelastic foundation is investigated in this paper, considering both exposure to thermal environment and transverse harmonic excitation. First, according to the Hamilton principle and nonlocal elastic theory, a dynamic model of the composite nanoplate is established by a group of nonlinear partial differential equations. Through the Galerkin method, the simply supported partial differential equations form of the composite nanoplate system is simplified to the form of an asymmetric Duffing-Helmholtz oscillator. Then, the dynamic mechanism of the composite nanoplate system containing a quadratic nonlinear term is revealed, and the influences of nonlocal parameter, temperature, viscoelastic foundation, thickness, aspect ratio and external voltage on the nonlinear vibration of the system are numerically analyzed comprehensively. Moreover, the effect of wave number on nonlinear vibration compared with the first-order wavenumber is emphasized. It is anticipated that the dynamic results of the present work would provide the theoretical basis for the experimental characterization of the mechanical properties of piezoelectric-graphene composite nanoresonators. [Figure not available: see fulltext.].