Instability of nonlinear viscoelastic plates

This paper investigates the instability of an isotropic, homogeneous, simply supported rectangular plate subjected to a prescribed periodic in-plane load. The material is assumed to be viscoelastic and obey the Leaderman nonlinear constitutive relation. The equation of motion is derived as a nonlinear integro-partial-differential equation, and is simplified into a nonlinear integro-differential equation by the Galerkin method. The averaging method is developed to establish the condition of instability. Numerical results are presented to compare with the analytical ones.