Non-linear Response Of Predeformed Plates Subject To Harmonic In-plane Edge Loading

Abstract

Following discretization, a non-linear ordinary differential equation of motion is obtained that describes the forced response of simply supported, prodeformed plates. The excitation, which derives from harmonically varying in-plane edge loading, results in both external and parametric excitation. The equation of motion also includes the quadratic and cubic non-linearities associated with mid-plane stretching. Periodic solutions and their stability are determined by using the harmonic balance method. By varying the magnitude of predeformation, these solutions display two limiting types of behavior. Plate response is driven mainly through external excitation for "large" predeformation and mainly through parametric excitation for small predeformation. The solutions capture the interaction between parametric and external excitation for intermediate predeformation which causes a change in stability of one solution. This change in stability leads to an instability region for the limiting case of pure parametric excitation (vanishing predeformation).