Modeling and Numerical Simulation of Sound Radiation by the Boundary Element Method

Authors: Costa, E.S., Borges, E.N.M., Afonso, M.M.

Abstract:

The modeling of sound radiation is of fundamental importance for understanding the propagation of acoustic waves and, consequently, develop mechanisms for reducing acoustic noise. The propagation of acoustic waves, are involved in various phenomena such as radiation, absorption, transmission and reflection. The radiation is studied through the linear equation of the acoustic wave that is obtained through the equation for the Conservation of Momentum, equation of State and Continuity. From these equations, is the Helmholtz differential equation that describes the problem of acoustic radiation. In this paper we obtained the solution of the Helmholtz differential equation for an infinite cylinder in a pulsating through free and homogeneous. The analytical solution is implemented and the results are compared with the literature. A numerical formulation for this problem is obtained using the Boundary Element Method (BEM). This method has great power for solving certain acoustical problems in open field, compared to differential methods. BEM reduces the size of the problem, thereby simplifying the input data to be worked and reducing the computational time used.

Keywords: Acoustic radiation, boundary element

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1074349

References:

[1] C. A. Brebbia, S. Walker, Boundary Element Techniques in Engineering, 1980.
[2] G. Chertock, "Sound Radiation from Vibrating Surfaces", The Journal of the Acoustical Society of America, Volume 36, Número 7, 1964, Páginas 1305 - 1313.
[3] R.D. Ciskowski, , C. A. Brebbia, Boundary Element Methods in Acoustics. Southampton-Boston: Computational Mechanics Publications, 1991.
[4] L. E. Kinsler, A.R Coppens, A.B. Sanders , J.V. Fundamentals of Acoustics. New York: John Wiley & Sons, J. V. 1982.
[5] G. S. Papini," Numerical Studies of Acoustics Barriers". Master Thesis, UFMG, Belo Horizonte, 1999.
[6] W. S. Yoon,J. M. Park, W. Eversman , " Two- Dimensional radiation and scattering at short wave length", Journal of Vibration and Acoustics, V. 11, 19902.
[7] L. J. Ziomek, Fundamentals of Acoustic Field Theory and Space-Time Signal Processing. Boca Raton: CRC Press, 1995.