href="#u543e5334-08d7-564f-84a4-f3aa03bc5f72">Chapter 10 of this book.).
The boundary element method (BEM) was developed a little later than the FEM. In the BEM approach the elements are described on the boundary surface only, which reduces the computational dimension of the problem by one. This correspondingly produces a smaller system of equations than the FEM. BEM involves the use of a surface mesh rather than a volume mesh. BEM, in general, produces a smaller set of equations that grows more slowly with frequency, and the resulting matrix is full; whereas the FEM matrix is sparse (with elements near and on the diagonal). Thus computations with FEM are generally less time‐consuming than with BEM. For sound propagation problems involving the radiation of sound to infinity, the BEM is more suitable because the radiation condition at infinity can be easily satisfied with the BEM, unlike with the FEM. However, the FEM is better suited than the BEM for the determination of the natural frequencies and mode shapes of cavities (See Chapter 10 of this book.).
Recently, FEM and BEM commercial software has become widely available. The FEM and BEM are described in Refs. [35, 36] and in chapters 12 and 13 in the Handbook of Acoustics [1].
3.19.3 Acoustic Modeling Using Equivalent Circuits
Electrical analogies have often been found useful in the modeling of acoustical systems. There are two alternatives. The sound pressure can be represented by voltage and the volume velocity by current, or alternatively the sound pressure is replaced by current and the volume velocity by voltage. Use of electrical analogies is discussed in chapter 11 of the Handbook of Acoustics [1]. They have been widely used in loudspeaker design and are in fact perhaps most useful in the understanding and design of transducers such as microphones where acoustic, mechanical, and electrical systems are present together and where an overall equivalent electrical circuit can be formulated (see Handbook of Acoustics [1], chapters 111–113).
Beranek makes considerable use of electrical analogies in his books [10, 11]. In chapter 14 in the Handbook of Acoustics [1] their use in the design of automobile mufflers is described. Chapter 10 in this book also reviews the use of electrical analogies in muffler and silencer acoustical design.
References
1 1 Crocker, M.J. (ed.) (1998). Handbook of Acoustics. New York: Wiley.
2 2 Malecki, I. (1969). Physical Foundations of Technical Acoustics. Oxford: Pergamon Press.
3 3 Skudrzyk, E. (1971). The Foundations of Acoustics. New York: Springer (reprinted by the Acoustical Society of America in 2008).
4 4 Crocker, M.J. and Price, A.J. (1975). Noise and Noise Control, vol. I. Cleveland, OH: CRC Press.
5 5 Lighthill, M.J. (2001). Waves in Fluids, 2e. Cambridge: Cambridge University Press.
6 6 Pierce, A.D. (1981). Acoustics: An Introduction to Its Physical Principles and Applications. New York: McGraw‐Hill (reprinted by the Acoustical Society of America, 1989).
7 7 Crocker, M.J. and Kessler, F.M. (1982). Noise and Noise Control, vol. II. Boca Raton, FL: CRC Press.
8 8 Morse, P.M. and Ingard, K.U. (1986). Theoretical Acoustics. Princeton, NJ: Princeton University Press.
9 9 Junger, M.J. and Feit, D. (1986). Sound, Structures, and Their Interaction. Cambridge, MA: MIT Press.
10 10 Beranek, L.L. (1986). Acoustics. New York: Acoustical Society of America (reprinted with changes).
11 11 Beranek, L.L. (1988). Acoustical Measurements, rev. ed. New York: Acoustical Society of America.
12 12 Crighton, D.G., Dowling, A.P., Ffowcs Williams, J.E. et al. (1992). Modern Methods in Analytical Acoustics. Berlin: Springer‐Verlag.
13 13 Fahy, F.J. (1995). Sound Intensity, 2e. London: E&FN Spon, Chapman & Hall.
14 14 Fahy, F.J. and Walker, J.G. (eds.) (1998). Fundamentals of Noise and Vibration. London and New York: E/FN Spon.
15 15 Filippi, P., Habault, D., Lefebvre, J., and Bergassoli, A. (1999). Acoustics: Basic Physics Theory & Methods. San Diego, CA: Academic Press.
16 16 Kinsler, L.E., Frey, A.R., Coppens, A.B., and Sanders, J.V. (1999). Fundamentals of Acoustics, 4e. New York: Wiley.
17 17 Blackstock, D.T. (2000). Fundamental of Physical Acoustics. New York: Wiley.
18 18 Bruneau, M. and Scelo, T. (2006). Fundamentals of Acoustics. London: ISTE.
19 19 Crocker, M.J. (1997). Encyclopedia of Acoustics. New York: Wiley.
20 20 Fuller, C. (2007). Active vibration control. In: Handbook of Noise and Vibration Control (ed. M.J. Crocker), 770–784. New York: Wiley.
21 21 Nelson, P.A. (2007). Sound sources. In: Handbook of Noise and Vibration Control (ed. M.J. Crocker), 43–51. New York: Wiley.
22 22 Jacobsen, F. (2007). Sound intensity measurements. In: Handbook of Noise and Vibration Control (ed. M.J. Crocker), 534–548. New York: Wiley.
23 23 Kuttruff, K.H. (2007). Sound propagation in rooms. In: Handbook of Noise and Vibration Control (ed. M.J. Crocker), 52–68. New York: Wiley.
24 24 Hansen, C.H. (2007). Room acoustics. In: Handbook of Noise and Vibration Control (ed. M.J. Crocker), 1240–1246. New York: Wiley.
25 25 Manning, J.E. (2007). Statistical energy analysis. In: Handbook of Noise and Vibration Control (ed. M.J. Crocker), 241–254. New York: Wiley.
26 26 Hansen, C.H. (2007). Sound absorption in rooms. In: Handbook of Noise and Vibration Control (ed. M.J. Crocker), 1247–1256. New York: Wiley.
27 27 Guyader, J.‐L. (2007). Sound radiation from structures and their response to sound. In: Handbook of Noise and Vibration Control (ed. M.J. Crocker), 79–100. New York: Wiley.
28 28 Ver, I.L. and Holmer, C.I. (1971). Interaction of sound waves with solid structures. In: Noise and Vibration Control (ed. L.L. Beranek), 270–361. New York: McGraw‐Hill.
29 29 Pierri, R.A. (1977) Study of a dynamic absorber for reducing the vibration and noise radiation of plate‐like structures. MSc thesis. University of Southampton.
30 30 Braun, S.G., Ewins, D.J., and Rao, S.S. (2001). Encyclopedia of Vibration. San Diego, CA: Academic.
31 31 Fahy, F.J. and Gardonio, P. (2007). Sound and Structural Vibration – Radiation, Transmission and Response, 2e. Oxford: Academic Press.
32 32 Bies, D.A. and Hansen, C.H. (2009). Engineering Noise Control – Theory and Practice, 4e. London and New York: Spon Press.
33 33 Fahy, F.J. (2001). Foundations of Engineering Acoustics. San Diego, CA: Academic Press.
34 34 Attenborough, K. (2007). Sound propagation in the atmosphere. In: Handbook of Noise and Vibration Control (ed. M.J. Crocker), 67–78. New York: Wiley.
35 35 Astley, R.J. (2007). Numerical acoustical modeling (finite element modeling). In: Handbook of Noise and Vibration Control (ed. M.J. Crocker), 101–115. New York: Wiley.
36 36 Herrin, D.W., Wu, T.W., and Seybert, A.F.
