Effect of thickness deformation on large-amplitude vibrations of functionally graded rectangular plates

Nonlinear forced vibrations of moderately thick functionally graded (FG) rectangular plates are investigated by considering higher-order shear deformation theories that take into account the thickness deformation effect. The geometrically nonlinear strain–displacement relationships are derived retaining full nonlinear terms in the in-plane and transverse displacements and the three-dimensional constitutive equations are used by removing the assumption of zero transverse normal strain. Both simply supported movable and immovable boundary conditions are considered at the plate edges. The equations of motion are obtained by using multi-modal energy approach. A code based on pseudo arc-length continuation and collocation scheme is utilized for numerical continuation and bifurcation analysis. Results show that higher-order thickness deformation theories yield a significant accuracy improvement for nonlinear vibrations of highly pressurized functionally graded plates.