An acoustic modeling of the three-dimensional annular segment cavity with various impedance boundary conditions

Abstract

A three-dimensional Fourier series method (3D-FSM) is applied to study the acoustic characteristics of annular segment acoustic cavity with various impedance boundary conditions. The formulation is constructed to describe the cavity system based on the energy principle. Under the framework of this paper, the admissible sound pressure function is generally set, regardless of boundary conditions, to a 3D Fourier cosine series and six supplementary functions. These supplementary functions can eliminate the discontinuous or jumping phenomenon in the boundaries. All the series expansion coefficients can be obtained through the Rayleigh-Ritz technique. The results obtained by the present method in this paper show good convergence. The accuracy of the present method is verified by being compared with the exact solution and the finite element method (FEM). The natural frequencies and modal shapes of the annular segment cavity are studied. The sound pressure response is investigated under the excitation of a monopole source inside the cavity. In this paper, some results of the acoustic characteristics of the cavity with various geometric parameters and boundary conditions are obtained, such as angle, radius ratio, impedance value and the number of impedance wall. These results provide a benchmark for the future researches. Keywords: Fourier series, Annular segment cavity, Impedance wall, Rayleigh-Ritz technique