Nonlinear vibration response of a rectangular tube with a flexible end and non-rigid acoustic boundaries

This paper addresses the analysis for the nonlinear vibration response of a rectangular tube with a flexible end and non-rigid acoustic boundaries. The structural-acoustic modal formulations are developed from the Duffing differential equation and wave equation, which represent the large-amplitude structural vibration of a flexible panel coupled with a cavity. This problem considers both non-rigid acoustic boundary and structural cubic nonlinearity. The multi-level residue harmonic balance method is employed for solving the nonlinear coupled differential equations developed in the problem. The results obtained from the proposed method and numerical method are generally in good agreement. The effects of excitation magnitude, tube length, and phase shift parameter, etc., are examined.