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

摘要

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.