Accurate backbone curves for large-amplitude vibrations of imperfect rectangular plate with viscous damping

This paper deals with the solution of modified-Duffing ordinary differential equation for large-amplitude vibrations of imperfect rectangular plate with viscous damping. Lindstedt's perturbation technique and Runge-Kutta method are applied. The results for both methods are presented and compared for a validity check. It is proved that Lindstedt’s perturbation technique only works accurately for a small range of vibration amplitude. For a structure with a sufficiently large geometric imperfection, the well-known softenspring to harden-spring transforming backbone curve is confirmed and better developed. Although the softening to hardening behavior occurs twice in one backbone curve, the turning points share the same vibration frequency. Yet the amplitude for turning points varies due to the existence of imperfection. Moreover, the effect of damping ratio on vibration mode and vibration amplitude is studied. The usual nonlinear vibration tends to behave more linearly under the effect of large damping.