A method to compute the radiated sound power based on mapped acoustic radiation modes

Application of modal expansion approach for the exterior acoustic field has drawn wide research interests in recent years. This is primarily due to the acoustic radiation modes (ARM) that can diagonalize the impedance matrix, hence significantly simplifying the computation of radiated sound power. The orthogonal ARM are typically calculated via a standard eigenvalue analysis of the impedance matrix, which normally leads to numerical difficulties especially for wideband frequency and large scale problems. In this paper, a theory of mapped ARM is proposed to avoid the cumbersome computation of ARM for convex structures. A mapping relationship between the ARM on the surface of an equivalent spherical source and the mapped ARM on the surface of a convex structure is obtained based on the equivalent source method, multipole expansion method, and boundary integral method. Furthermore, analytical expressions for the radiated sound power of structures vibrating in its mapped ARM as well as that of spheres are derived. Finally, a simple method is proposed to approximate the radiated sound power based on the modal decomposition method and the mapping relationship. Numerical simulations are conducted to validate the accuracy and efficiency of the proposed approach, and different vibrating structures with various geometries are considered. Results demonstrate that the proposed methodology for calculating the radiated sound power of convex structures is very efficient and accurate as compared with the traditional approach.