Efficient analytical method for computing the acoustic field inside enclosures with a mixed rectangular-cylindrical geometry

Abstract

Enclosures with a mixed rectangular-cylindrical geometry are common in sacred, historic and modern buildings. Therefore, obtaining efficient analytical formulas for describing the sound radiation inside such structures is of practical importance. These formulas can be implemented in open-source software and can aid in the analysis of acoustic fields. In this study, the problem of sound radiation by a point source located inside a rectangular enclosure with a sound-absorbing quarter-cylindrical ceiling was analytically solved. The formulas presented in this paper can also be used to obtain the eigenfrequencies and eigenfunctions. To obtain the analytical solution, two connected subregions, namely rectangular space, and quarter-cylinder, were considered, and the continuity conditions were imposed on the region’s coupling interface. The acoustic field was described using the solution for a rigid-walled room and the additional components containing the Fourier and Dini series. These components allow the solution to satisfy the impedance boundary condition and the continuity conditions. The formulas and their computer implementation were validated using the finite element method (FEM). A good agreement was achieved between results given by both methods. The numerical analysis demonstrated that the use of the formulas is less time-consuming than using FEM when the frequency is greater than 150 Hz. Moreover, compared to FEM, the analytical solution can be applied to higher frequencies for which the use of FEM requires hardware with high computing capability.