Nonlinear dynamic analysis and vibration of shear deformable piezoelectric FGM double curved shallow shells under damping-thermo-electro-mechanical loads

Abstract Nonlinear dynamic analysis and vibration of imperfect functionally graded materials (FGM) thick double curved shallow shells with piezoelectric actuators on elastic foundations subjected to the combination of electrical, thermal, mechanical and damping loading are investigated in this paper. Material properties of FGM shells are assumed to be temperature dependent and graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The governing equations are established based on Reddy’s higher order shear deformation theory that includes thermo-piezoelectric effects and are solved by the stress function, the Galerkin method and fourth-order Runge–Kutta method. In numerical results, the effects of geometrical parameters; the material properties; imperfections; elastic foundations; electrical, mechanical, thermal and damping loads on the nonlinear dynamic analysis and nonlinear vibration of the FGM hybrid double curved shallow shells are discussed.