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Two-dimensional resonators with small openings

Published online by Cambridge University Press:  17 February 2009

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Abstract

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The acoustic response of a two-dimensional nearly-closed cavity to an excitation through a small opening is examined, using the method of matched asymptotic expansions. The Helmholtz mode of vibration is discussed using a low-frequency expansion of the velocity potential in the cavity interior. The variation in frequency and magnitude of the resonator response is explored, both for the Helmholtz and the natural-frequency modes.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1982

References

[1]Gradshteyn, I. S. and Ryzhik, I. M., Tables of integrals, series and products (Academic Press, New York, 4th edition, 1970).Google Scholar
[2]von Helmholtz, H., “Theorie der Luftschwingungen in Röhren mit offenen Enden”, Crelle 57 (1860), 172.Google Scholar
[3]Lee, J.-J., “Wave induced oscillations in harbours of arbitrary shape”, Cal. Inst. Tech. W. M. Keck Lab. Hydraul. & Wat. Res. Rep. KH–R–20 (1969), 1266.Google Scholar
[4]Lee, J.-J., “Wave induced oscillations in harbours of arbitrary geometry”, J. Fluid Mech. 45 (1971), 375394.Google Scholar
[5]Miles, J. W., “Resonant response of harbours: an equivalent-circuit analysis”, J. Fluid Mech. 46 (1971), 241265.Google Scholar
[6]Miles, J. W., “Harbor seiching”, Annual Rev. Fluid Mech. 6 (1974), 1735.CrossRefGoogle Scholar
[7]Miles, J. W. and Lee, Y. K., “Helmholtz resonance of harbours”, J. Fluid Mech. 67 (1975), 445464.Google Scholar
[8]Rayleigh, Lord, “On the theory of resonance”, Phil. Trans. Roy. Soc. 161 (1870), 77118.Google Scholar
[9]Lord, Rayleigh, The theory of sound (Dover, New York, 1945), Volume 2.Google Scholar
[10]Tuck, E. O., “Matching problems involving flow through small holes”, Adv. Appl. Mech. 15 (1974), 1117.Google Scholar