Nonlinear free vibration analysis of a plate-cavity system

• Variational iteration method predicts nonlinear eigen-frequencies of a plate-cavity.
• Eigen-frequency of a plate-cavity system is remarkably influenced by initial condition.
• Increasing the initial conditions enhance the frequency ratio of the first mode.
• Higher longitudinal modes are more influenced by A11 than their own initial amplitude.
• Both vibro-acoustic coupling and inter-modal coupling should be taken into account.

Free vibration of a plate-cavity system is analytically studied in this paper. For this purpose, a rectangular enclosure composed of one flexible and five rigid walls are taken into account. The flexible wall is modeled by the Von-Karman plate theory and the Galerkin method is employed to derive interior acoustic pressure and subsequent equations of motion. Harmonic balance approach, variational iteration method (VIM) and direct integration method are employed to determine nonlinear natural frequencies of the coupled system. A parametric study is then carried out and effects of different parameters on the value of frequency ratio are studied.