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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.

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In this research, we analyze the acoustic–vibration coupling of liquid-filled cylindrical shells under complex excitations. A calculation model to determine the acoustic characteristics and steady-state response of a cylindrical shell coupled to an acoustic cavity is proposed. The displacement and sound pressure of the cylindrical shell are described by a Chebyshev–Fourier series in three dimensions. The uncertain expansion coefficient is determined with a Rayleigh–Ritz model. The accuracy and convergence of this method are compared with those of the finite element method. The spring constraint is applied to simulate arbitrary boundary parameters. The impact of these parameters on the coupled natural frequency is analyzed. Finally, the steady-state response of a coupled system for various excitation parameters is analyzed.