Methods in Solving the Wave Equations for a Loudspeaker

Abstract:

This paper introduces several methods in solving the wave equations for a loudspeaker. The separation of variables method is very common for solving constant coefficient linear partial differential problems. The finite difference method has been the main method of numerical computation in early work. The direct method is to formulate the boundary integral equation and can be solved using a direct time integration procedure. There are also some transform methods such as Fourier, Laplaces and wavelet transforms etc. to solve the wave equations. The retarded potential technique to solve the wave problems numerically was first used in the early 1960s. Since then, many authors have worked on the method and its applications.

• Periodical: Advanced Materials Research (Volumes 756-759)
• Pages: 2922-2925
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.756-759.2922
• Online since: September 2013
• Authors: Jing Zeng, Hui Wang, Jun Yu Dong
• Keywords: Finite Difference, Integral, Loudspeaker, Retarded Potential, Separation of Variables, Transform

References

[1] Chester Clive R. (1971). Techniques in Partial Differential Equations. McGraw-Hill Inc.

[2] Carrier George F. (1976). Partial Differential Equations: theory and technique. New York Academic Press.

[3] Jódar L. and Almenar P. (1996). Numerical Solutions of Time Dependent Mixed Partial Differential Problems. Computers Math. Applic. V32, N2, pp.5-19.

DOI: 10.1016/0898-1221(96)00099-5

[4] Mitchell A.R. and Griffiths D.F. (1980). The Finite Difference Method in Partial Differential Equations. John Wiley and Sons.

[5] Schedin S., Lambourge C. and Chaigne A. (1999). Transient sound fields from impacted plates: comparison between numerical simulations and experiments. Journal of Sound and Vibration 221(3), pp.471-490.

DOI: 10.1006/jsvi.1998.2004

[6] Villarreal Alberto and Scales John A. (1997). Distributed three-dimensional finite-difference modelling of wave propagation in acoustic media. Computers in Physics, V. 11, N. 4, pp.388-399.

DOI: 10.1063/1.168610

[7] Nardini D. and Brebbia C.A. (1985).

[8] Tanaka Masa., Matsumoto T. and Moradi M. (1995). Application of boundary element method to 3-D problems of coupled thermoelasticity. Engineering Analysis with Boundary Elements 16, pp.297-303.

DOI: 10.1016/0955-7997(95)00074-7

[9] Brebbia C.A. and Nardini D. (2000). Dynamic analysis in solid mechanics by an alternative boundary element procedure. Engineering Analysis with Boundary Elements 24, pp.513-518.

DOI: 10.1016/s0955-7997(00)00031-x

[10] Gaul L. and Wenzel W. (2001). Acoustic calculations with the hybrid boundary element method in time domain. Engineering Analysis with Boundary Elements 25, pp.259-265.

DOI: 10.1016/s0955-7997(01)00021-2

[11] Duddeck Fabian M.E. (2002). Fourier BEM, Generalization of Boundary Element Methods by Fourier Transform. Springer Verlag Berlin.

[12] Geaves G.P., Moore J.P., Henwood D.J. and Fryer P.A. (2001). Verification of an approach for transient structural simulation of loudspeakers incorporating damping. Audio Engineering Society Convention Paper 5320, pp.1-12.

[13] Hong Tae-Kyung and Kennett B. L. N. (2002). On a wavelet-based method for the numerical simulation of wave propagation. Journal of Computational Physics 183, pp.577-622.

DOI: 10.1006/jcph.2002.7202