Sound transmission characteristics of a plate backed by an irregular cavity

Abstract

The study of the coupling cavity provides an effective theoretical reference for the acoustic design. However, most of the previous studies are based on idealized models and there is little research on the sound radiation power about the irregular shapes. The work in this paper achieves the generalization of the model and explores the impact of irregular back cavities on the sound radiation of the plate structures. The influence on the results of the sound insulation performance testing of the plate is also investigated when irregular cavities involved. The displacement of the plate and the sound pressure inside the cavities are expressed as multidimensional Fourier series with additional terms, which will contribute to maintaining the continuity of pressure and velocity at the boundaries. The sound field of the irregular cavity is considered as a unit cubic one in a new coordinate system by coordinate transformation method. The arbitrary boundary of the cavities is realized by adding the energy terms of impedance into the Lagrange equation. The Hamilton’s principle is employed to realize the complete coupling between the plate and the sound fields on both sides. The sound radiation power of the plate can be obtained by using the Rayleigh integral. By using Fast Cosine Transform, the quadruple integrals of the radiation power are simplified to improve accuracy and efficiency of the calculation. Numerical results from the analytical approach are compared with those given by Finite Element Analysis (FEM) to guarantee the rightness and validity of the models. Moreover, experimental results are also given to discuss the reasons of the bias between theory and practice.