Abstract
The parametric resonance and other dynamic instabilities of a rectangular plate with initial geometric imperfections acted upon by parametric excitation have been investigated. The temporal equations of motion describing the non-linear behavior of these plates for large oscillations are solved using a direct integration. Results are compared with those obtained from an approximate analytical method. For a structure with a sufficiently large initial imperfection, the soft-spring nature of parametric resonance is confirmed for small vibration amplitudes, followed by a hard-spring behavior for large vibration amplitudes. However, the temporal response of the imperfect structure displays a predominant inward deflection. This phenomenon increases with an augmentation of the imperfection amplitude. Moreover, some resonances not predicted by analytical methods are observed. Besides the possibility of principal parametric resonance, many internal resonances may be observed during a passage through a single parametric resonance.
