Modeling and vibro-acoustic analysis of elastically restrained panel backed by irregular sound space

A general analytical method is developed for the natural features and vibro-acoustic response analysis of an arbitrarily restrained rectangular plate backed by an irregular cavity. The modeling of the structure and the sound space are developed by employing the variational theory based on the sub-structure method. The irregular enclosure is disassembled into sub-cavities and the coupling formulae are deduced. The continuity conditions of both sound pressure and particle velocity at the coupling interface are exactly satisfied. The variational expressions of elastic boundary conditions of the panel are presented and thus the classical boundary conditions can be easily obtained by assigning appropriate elastic coupling coefficients. The vibration and sound pressure solutions are obtained by performing the Rayleigh-Ritz procedure. The accuracy and efficiency of the present method are validated by checking the present results against the finite element method (FEM) results for systems separately with right-angled trapezoidal and concave curved trapezoidal sub-cavity. It is shown that the present method is suitable for a system with an irregular cavity and an elastically restrained plate by exhibiting satisfactory accuracy, fast convergence speed while requiring small computation effort.