Large-amplitude vibration of imperfect angle-ply laminated rectangular plates with four boundary conditions

This paper solves the modified-Duffing ordinary differential equation for the large-amplitude vibration problem of imperfect angle-ply laminated rectangular plate. Two in-plane and two out-of-plane constraints are considered to form four boundary conditions. The initial condition is chosen to be initial vibration amplitude. To solve this angle-ply laminated rectangular plate vibration problem, Lindstedt's perturbation technique and Runge-Kutta method are applied. The solution from both methods are plotted and compared for a validity check. Lindstedt's perturbation technique is proved to be accurate for a sufficiently small vibration amplitude especially when imperfection exists. The results from Runge-Kutta method are plotted to form the typical backbone curves.