NONLINEAR RESPONSE OF PREDEFORMED PLATES SUBJECT TO HARMONIC INPLANE EDGE LOADING

Following discretization, a non-linear ordinary differential equation of motion is obtained that describes the forced response of simply sup ported, predeformed plates. The excitation, which derives from harmoni cally varying in-plane edge loading, results in both external and para metric excitation. The equation of motion also includes the quadratic and cubic non-linearities associated with mid-plane stretching. Period ic solutions and their stability are determined by using the harmonic balance method. By varying the magnitude of predeformation, these solu tions display two limiting types of behavior. Plate response is driven mainly through external excitation for ''large'' predeformation and m ainly through parametric excitation for small predeformation. The solu tions capture the interaction between parametric and external excitati on for intermediate predeformation which causes a change in stability of one solution. This change in stability leads to an instability regi on for the limiting case of pure parametric excitation (vanishing pred eformation).