Abstract
This paper presents a method to predict the acoustic characteristics and steady-state responses of a flexible plate strongly coupled with rectangular cavity based on energy principle theory and Legendre polynomial series. First, the displacement of the plate and the sound pressure in the cavity are constructed in the form of two-dimensional and three-dimensional Legendre polynomial series, respectively. The unknown expansion coefficients are obtained using the Rayleigh–Ritz technique based on the energy expressions for the strongly coupled plate-cavity system. The accuracy, convergence, and efficiency of the present method are verified by comparing with the results available in the FEM and literature. Finally, the effects of the structural boundary conditions, cavity depth, and structural length-width ratio on the coupling natural frequency and the steady-state responses under three excitation conditions are analyzed.
Highlights
In order to express the effect of acoustic cavity on structural vibration, Fahy [5] proposed the concept of modal coupling, which uses modal coupling coefficients to characterize the interaction between structure and cavity
The results of the present method and FEM are in good agreement, which on the one hand further demonstrates the accuracy of present method in predicting the acoustic characteristics of strongly coupled systems
A strongly coupled structure-acoustic model for a rectangular cavity and its flexible wall is proposed, and the displacement of the plate and the sound pressure in the cavity are developed based on energy principle theory and Legendre polynomial series. e acoustic characteristics and the forced response of the coupled system are obtained using the Rayleigh–Ritz technique
Summary
Dowell gave the theoretical solution of structural displacement and sound pressure in form of Fourier series On this basis, Pretlove [3, 4] proposed to calculate the vibration response of the structure by using the structural modes in vacuum and analyzed the effect of the cavity depth on the vibration and acoustical response. The computational cost of IFM and CPSM is high [20, 21] Inspired by these limitations, based on the principle of energy, the acoustical characteristics of the strongly coupled plate-cavity system with arbitrary structure boundary constraints is analyzed by using Legendre polynomial series in this paper.
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