Double harmonically excited nonlinear vibration of viscoelastic piezoelectric nanoplates subjected to thermo-electro-mechanical forces

The objective of the present paper is to comprehensively study the nonlinear frequency response of viscoelastic piezoelectric nanoplates exposed to dual harmonic external excitation and thermo-electro-mechanical loads. To achieve this goal, firstly, a piezoelectric nanoplate resting on a viscoelastic foundation is modeled. Secondly, using the nonlocal piezoelectricity theory, Kelvin–Voigt model, von Karman nonlinear relations and Hamilton’s principle, the nonlinear governing differential equation of motion is derived. In the next step, employing the Galerkin technique and multiple time scales method, the partial differential equation is transformed to an ordinary one and solved. Finally, the modulation equation of viscoelastic piezoelectric nanoplates for combinational excitation is obtained. Emphasizing the effect of dual harmonic excitation and thermo-electro-mechanical loads on nonlinear frequency response of the system, jump and resonance phenomena are discussed. A detailed parametric study is conducted to examine the effect of nonlinearity, damping coefficient, nonlocal parameter, combinational excitation, electric voltage, initial stress and thermal environment.