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

Abstract

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 superharmonic frequency components for the plate at ambient temperature, and the subharmonic frequency components in the thermal environments.