On the Occurrence of Simultaneous Resonances in Parametrically-Excited Rectangular Plates

Abstract

The present work deals primarily with the problem of the occurrence of simultaneous resonances in parametrically-excited rectangular plates. The analysis is based on the dynamic analog of the von Karman’s large-deflection theory and the governing equations are satisfied using the orthogonality properties of the assumed functions. The temporal response of the damped system is determined by the generalized asymptotic method and various types of simultaneous resonances are investigated. An experimental investigation is performed to verify the analytical predictions and to possibly discover new phenomena not predicted by the theory. Experiments are conducted for four different sets of boundary conditions. Analytically defined simultaneous resonances are experimentally observed and isolated.

Parametric combination resonance instability characteristics of laminated composite curved panels with circular cutout subjected to non-uniform loading with damping

“…Takahashi and Konishi [33] analyzed the simple as well as combination resonances of rectangular plates subjected to an in-plane sinusoidal linearly varying force by using harmonic balance method. Ostiguy et al [34] investigated the occurrence of simultaneous and combination resonances in multi-degree-of-freedom systems subjected to parametric excitation by using the generalized asymptotic method. Lee and Kim [35] studied the combination resonances of a clamped circular plate with three mode interaction by using the method of multiple scales (MMS).…”

Dynamic Stability and Nonlinear Parametric Vibrations of Rectangular Plates

“…An internal resonance is possible when two or more natural frequencies are commensurable or almost commensurable. When an internal resonance coincides with a parametric resonance, the combination of the two types gives rise to simultaneous resonances 39,40 . This kind of resonances is characterized by the fact that the system in question vibrates simultaneously in more than one normal mode and at different frequencies, although only one of the modes is directly excited by the parametric excitation.…”

“…Analytical and experimental results on the stationary and non-stationary parametric responses of nonlinear rectangular plates were presented by Ostiguy and Evan-Iwanowski 37,38 . Recently, Ostiguy, Samson and Nguyen 39,40 performed an analytical and experimental investigation of the occurrence of simultaneous and combination resonances in parametrically excited rectangular plates.…”

“…One of the first theories concerning the effects of geometric imperfections on the parametric vibration of rectangular plates is due to Silver 54 39,40 constitute an original and significant contribution.…”

More Details About the Interaction of Forced and Parametric Resonances Arising From in-Plane Excitation of Imperfect Rectangular Plates

“…However, when both of them are partially or totally overlapping, the global response of the plate becomes unpredictable. Experimental evidence of simultaneous and combination resonances, due to the interaction of forced and parametric vibrations, presented by Ostiguy [1], Ostiguy et al [3], constitutes an original and signi"cant contribution.…”