Vibro–Acoustic Analysis of the Strong Coupling System with an Elastically Restrained Rectangular Plate Backed by a Trapezoidal Cavity

Abstract

The vibro–acoustic strong coupling problem between the panel and cavity widely exists in the industry. This paper developed a numerical method to study the natural characteristics and vibro–acoustic response of the strong coupling system with an elastically restrained rectangular plate backed by a trapezoidal cavity. The isoparametric transformation technique was used to normalize the trapezoidal cavity. The dynamical equations of the coupling system were derived using the energy principle and the Rayleigh–Ritz method with the Legendre polynomial series as trial functions. Then, the effects of structural boundary conditions and bevel angle on the natural frequencies of the system with the elastic plate on the top surface of the trapezoidal cavity were explored. The natural frequency increased with the number of structural support boundaries and the inclination angle of the trapezoidal cavity bevel. Besides, the steady-state response of the coupling system under different excitation conditions was investigated. Therefore, accurate prediction for steady-state response will provide ideas for noise control of the vibro–acoustic strong coupling problem.