Nonlinear Vibration Response of a Rectangular Tube with a Flexible End and Non-Rigid Acoustic Boundaries

Abstract

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.

Free Vibration Analysis of Nonlinear Structural-Acoustic System with Non-Rigid Boundaries Using the Elliptic Integral Approach

“…That is the rationale why this paper aims to study the effect of acoustic boundary condition. Although the structural acoustic research work in [9] considered a non-rigid boundary, it focused on the forced vibration responses of a long duct. To the best of the author's knowledge, it was the only one which considered the non-rigid boundary condition in structural acoustic research.…”

“…To the best of the author's knowledge, it was the only one which considered the non-rigid boundary condition in structural acoustic research. On the other hand, the solution method employed in [9] was the harmonic balance method. In fact, there have been numerous nonlinear structural vibration and nonlinear oscillation problems solved by the harmonic balance, perturbation, and multiple time scale methods (e.g., [10,11]).…”

“…Figure 1 shows the model considered in this study, which includes a large amplitude panel coupled with an acoustic cavity. The governing equation of the sound pressure field within the cavity is given by [7][8][9] (i.e., the well-known wave equation).…”