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This paper studies a nonlinear oscillation of a plate cavity system analytically. The system's nonlinear differential equations are described by a three-degree-of-freedom (3DOF) and subjected to parametric excitation forces. A second order approximate solutions of the system equations were sought using the multiple scale perturbation (MSPT). Some resonance cases were studied numerically. Additionally, the vibratory system's bifurcation behaviors and steady state solutions of the system parameters applying both phase-plane technique and frequency response equations near the simultaneous resonance were examined. The effects of some different parameters of system behavior were also studied numerically. Several confirmations were performed for analytical and numerical comparison results.

On the Nonlinear Vibrations and Stability Analysis of a Plate-Cavity System With a Nonlinear Restoring Force