Nonlinear vibration of piezoelectric graphene-reinforced composite laminated panels in thermal environment using Amabili-Reddy shear deformation theory

•Fourth-order shear deformation theory is applied for nanocomposite panels.•Piezoelectric layer: quadratic electric potential, Green-Lagrange strains, pyroelectric effects, open and closed circuits.•For the first time, the explicit forms of PDEs of motions are extracted.•For the first time, He variational method is extended for six-coupled PDEs.•Amabili-Reddy theory has less sensitivity to electric surface condition than FSDT. This work studies large amplitude free vibration of piezoelectric laminated doubly curved panels reinforced with zigzag/armchair graphene sheets under uniform temperature rise. Thermomechanical and kinematic relations are derived using refined Halpin-Tsai approach and Amabili-Reddy (fourth-order shear deformation) theory which remains all nonlinear terms in the in-plane displacements. The explicit form of the quadratic variation of electric potential with Green-Lagrange strains and pyroelectric effects under open and closed circuits are presented. As a first endeavor, the explicit forms of six-coupled PDEs of motions are extracted using Gibbs energy, Hamilton principle and Maxwell equation. For the first time, the eigenvalue problem is solved via the Galerkin and extended He variational method. To verify, linear frequencies of piezoelectric, graphene-reinforced composite and nonlinear frequencies of laminated composite plates are compared with available results and it is shown that Amabili-Reddy theory has less sensitivity to electric surface condition than first-order shear deformation theory. Parametric studies reveal that panels with low thickness of piezoelectric layer, closed circuit and high temperature show higher frequency ratios than other panels. Moreover, panels with BaTiO3 layers display more sensitivity to the amplitude and less sensitivity to electric surface condition than panels integrated with PZT-4 and PZT-5A layers in ambient temperature.