Accurate backbone curves and dynamic failure for large-amplitude axisymmetric vibrations of imperfect circular plates

Abstract

This paper deals with the solution of modified-Duffing ordinary differential equation for large-amplitude vibrations of imperfect circular plate. Four types of boundary conditions are considered as well as viscous damping. Lindstedt’s perturbation technique and Runge–Kutta method are applied. The solution from two methods are plotted and compared for a validity check. Lindstedt’s perturbation technique is proved to be accurate for sufficiently small vibration amplitude and imperfection. The results from Runge–Kutta method is plotted to form a backbone curve except for the case with clamped and zero radial stress boundary condition. Instead of expected softening–hardening process, the curve is only softening thus no longer backbone. More importantly, a dynamic failure is noticed when initial vibration amplitude grows under this boundary condition. A geometric imperfection will further help to trigger this failure at a smaller amplitude. This finding has served a new way to judge dynamic failure mode and is valuable for structure design concerning vibration.