Thermal effects on nonlinear vibrations of functionally graded doubly curved shells using higher order shear deformation theory

Geometrically nonlinear vibrations of functionally graded (FG) doubly curved shells subjected to thermal variations and harmonic excitation are investigated via multi-modal energy approach. Two different nonlinear higher-order shear deformation theories are considered and it is assumed that the shell is simply supported with movable edges. Using Lagrange equations of motion, the energy functional is reduced to a system of infinite nonlinear ordinary differential equations with quadratic and cubic nonlinearities which is truncated based on solution convergence. A pseudo-arclength continuation and collocation scheme is employed to obtain numerical solutions for shells subjected to static and harmonic loads. The effects of FGM power law index, thickness ratio and temperature variations on the frequency–amplitude nonlinear response are fully discussed and it is revealed that, for relatively thick and deep shells, the Amabili–Reddy theory which retains all the nonlinear terms in the in-plane displacements gives different and more accurate results.