Sound radiation from the plate backed by the rectangular cavity

Abstract

The radiation sound field of the plate with general boundary conditions backed by the acoustic cavity is investigated theoretically. The displacement function of the plate is generally expressed as a 2-D Fourier cosine series with additional terms. The addition terms could be used to accelerate the convergence rate of the present method and to account for the discontinuity of the displacement at the boundaries. The vibro-acoustic coupling between the vibration of the plate and the sound field on both sides of the plate is fully taken into consideration by adopting the Hamilton's principle. The sound pressure in the cavity is expressed as a 3-D Fourier series with additional terms which is used to account for the continuity between the velocity of the plate and the sound pressure on the plate. The sound radiation power of the plate can be obtained by using the Rayleigh integral. By means of Fast Cosine Transform, the quadruple integrals of the sound radiation power of the plate is reduced to several single integrals, which effectively avoids the time-consuming calculation. The influence of parameters on sound radiation power, such as boundary conditions, the sizes of the cavity, acoustic medium inside the cavity and the mounting position of the plate, are studied.