Nonlinear vibration of a composite plate to harmonic excitation with initial geometric imperfection in thermal environments

The paper focuses on the nonlinear dynamic response of a thermally loaded thin composite plate subjected to harmonic excitation. A theoretical formulation is derived in terms of assumed modes and an Airy stress function, which incorporates an initial global geometric imperfection. Contributions of in-plane boundary constraints due to surrounding thermal sealing materials are taken into accounted by giving equivalent in-plane boundary stiffness. The effects of the temperature, equivalent in-plane boundary stiffness and initial geometric imperfection on the dynamic behavior are investigated through a detail parametric study. It is shown that the critical buckling temperature of a perfect plate decreases with increasing the equivalent in-plane boundary stiffness significantly. A secondary stable equilibrium branch exists for an imperfect plate. The presence of the global imperfection postpones the onset of the critical state. The nonlinear dynamic response of the plate is a hardening-spring type in the pre-critical region due to one equilibrium state, and is a softening-type in the post-critical region because of two stable equilibria. The strain frequency response is dominated by the super-harmonic frequency components for the plate at ambient temperature, and the subharmonic frequency components in the thermal environments.