Analysis of Acoustic Characteristics of Arbitrary Triangular Prism and Quadrangular Prism Acoustic Cavities

Abstract

This paper proposes a method for the analysis of acoustic modals and steady-state responses of arbitrary triangular prism and quadrangular prism acoustic cavities based on the three-dimensional improved Fourier series. First, the geometric models of arbitrary triangular prism and quadrangular prism acoustic cavities are established. To facilitate the calculation, the bottom and top surfaces of the irregular cavity are converted into the unit square domain by a coordinate transformation. Internal sound pressure-admissible functions are constructed, and energy expressions are derived after coordinate transformation based on the three-dimensional improved Fourier series. The acoustic modals of arbitrary triangular prism and quadrangular prism acoustic cavities are obtained by the Rayleigh–Ritz technique. At the same time, a point sound source excitation is introduced into the cavity to further study the steady-state responses of prismatic acoustic cavities with different acoustic impedance boundary conditions. The reliability and universality of the method are verified by comparing with the finite element results. The method and results can provide some references and benchmarks for future research and application.

Study on Acoustic Characteristics of a Flexible Plate Strongly Coupled with Rectangular Cavity

“…where U P is the total acoustic potential energy of the flexible plate, T P is the total kinetic energy of the flexible plate, W P is the work done by the point force source, and W C2P represents the work done by sound pressure to the flexible plate [20]. eir specific expressions are…”

“…In order to investigate the acoustic characteristic of an elastically restrained plate coupled with an enclosure, Du et al [16][17][18][19] proposed an improved Fourier series by introducing auxiliary function to ensure the continuity of vibration velocity on the platecavity interface. Shi et al [20] used coordinate transformation to map irregular cavities to the unit square domain and studied its acoustic properties based on the three-dimensional improved Fourier series. On the basis, Chen et al [21,22] modeled the coupling system by replacing the improved Fourier series with Chebyshev polynomial series (CPSM), which was more concise and required less computation.…”

“…In the view of the existing literatures, different from the research on the weakly coupled panel-cavity system, the research on the strongly coupled plate-cavity system focuses on the system characteristics and less on the steadystate response. Meanwhile, the computational cost of IFM and CPSM is high [20,21]. Inspired by these limitations, based on the principle of energy, the acoustical characteristics of the strongly coupled plate-cavity system with arbitrary structure boundary constraints is analyzed by using Legendre polynomial series in this paper.…”

Analysis of the Vibro-Acoustic Behavior of a Stiffened Double Panel-Cavity System

“…Du et al [28] solved the general impedance boundary condition simulation problem of a rectangular acoustic cavity by the improved Fourier series method; later, they established the vibro-acoustic analysis model of a panelcavity coupled system [29]. Shi et al [30] used this method to analyze the acoustic modals and steady-state responses of triangular and quadrangular prism acoustic cavities. Zhang et al [31] used this method to analyze the vibro-acoustic analysis of an annular segment flexible panel-cavity coupled system.…”

Free vibration analysis of structural-acoustic coupled system using hybrid impedance and mobility approach

“…When the inclination is increased, the trapezoidal cavity-mode shape becomes complicated and unrecognizable [14]. Dongyan Shi et al proposed a method for the analysis of acoustic modals and steady-state responses of arbitrary triangular prism and quadrangular prism acoustic cavities based on the three-dimensional improved Fourier series [15].…”