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.
Highlights
In the well-known acoustic text book [1], an investigation of resonating tube/pipe accounted for the properties of the mechanical driver, which was driven by external excitation
The multi-level residue harmonic balance method, which was developed by Leung and Guo [8] in 2011, and modified by Hansan et al [9] in 2013, is employed to solve the nonlinear differential equations, which represent the large amplitude structural vibration of a flexible panel coupled with a cavity
It is shown that the 1st level 4 acoustic mode and two structural mode approach is good enough for convergent and accurate vibration amplitude solution
Summary
In the well-known acoustic text book [1], an investigation of resonating tube/pipe accounted for the properties of the mechanical driver, which was driven by external excitation. This paper would focus on structural nonlinearity and non-rigid acoustic boundary. The multi-level residue harmonic balance method, which was developed by Leung and Guo [8] in 2011, and modified by Hansan et al [9] in 2013, is employed to solve the nonlinear differential equations, which represent the large amplitude structural vibration of a flexible panel coupled with a cavity. When compared with the classical harmonic balance method, this harmonic balance method requires less computational effort. It is because it requires to solve one nonlinear algebraic equation and one set of linear algebraic equations only for obtaining each higher level solution to any desired accuracy. Parametric studies are performed and the effects of various parameters on the nonlinear vibration responses are investigated in detail
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