Hostname: page-component-848d4c4894-x24gv Total loading time: 0 Render date: 2024-05-17T12:27:39.410Z Has data issue: false hasContentIssue false
  • English
  • Français

The response of Helmholtz resonators to external excitation. Part 1. Single resonators

Published online by Cambridge University Press:  20 April 2006

Peter A. Monkewitz  and
Nghiem-Minh Nguyen-Vo
Peter A. Monkewitz
Affiliation:
Department of Mechanical, Aerospace and Nuclear Engineering, University of California at Los Angeles, CA 90024
Nghiem-Minh Nguyen-Vo
Affiliation:
Department of Mechanical, Aerospace and Nuclear Engineering, University of California at Los Angeles, CA 90024
Get access Rights & Permissions [Opens in a new window]

Abstract

The response of single two- and three-dimensional Helmholtz resonators subject to external excitation by a plane acoustic wave is studied. The inviscid linearized problem is solved by the matched-asymptotic-expansion technique in the low-frequency limit, i.e. when the characteristic neck dimension is small compared with the acoustic wavelength. The scale of the cavity is chosen such as to tune the system to the lowest Helmholtz mode. The results are compared with the classical lumped-element model, and refined expressions are derived for the effective mass (added length) and stiffness (effective cavity volume) of the resonator.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 151 , February 1985 , pp. 477 - 497
Copyright
© 1985 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abramowitz, M. & Stegun I. A.1968 Handbook of Mathematical Functions, 5th edn. Dover.
Carrier G. F., Shaw, R. P. & Miyata M.1971 The response of narrow-mouthed harbors in a straight coastline to periodic incident waves. Trans. ASME E: J. Appl. Mech. 38, 335–344.Google Scholar
Davy N.1944 The field between equal semi-infinite rectangular electrodes or magnetic pole pieces Phil. Mag. (7) 35, 819–840.Google Scholar
Dean P. D.1974 An in situ method of wall acoustic impedance measurements in flow ducts. J. Sound Vib. 34, 97–130.Google Scholar
Gradshteyn, I. S. & Ryzhik I. M.1965 Tables of Integrals, Series and Products. Academic.
Howe M. S.1979 The influence of grazing flow on the acoustic impedance of a cylindrical wall cavity. J. Sound Vib. 67, 533–544.Google Scholar
Ingard U.1953 On the theory and design of acoustic resonators. J. Acoust. Soc. Am. 25, 1037–1061.Google Scholar
Ingard, U. & Ising H.1967 Acoustic nonlinearity of an orifice. J. Acoust. Soc. Am. 42, 6–17.Google Scholar
Kevorkian, J. & Cole J. D.1981 Perturbation Methods in Applied Mathematics. Springer.
Lamb H.1945 Hydrodynamics. Dover.
Lesser, M. B. & Lewis J. A.1972a Application of matched asymptotic expansion methods to acoustics I: the Webster horn equation and the stepped duct. J. Acoust. Soc. Am. 51, 1664–1669.Google Scholar
Lesser, M. B. & Lewis J. A.1972b Application of matched asymptotic expansion methods to acoustics II: the open-ended duct. J. Acoust. Soc. Am. 52, 1406–1410.Google Scholar
Lesser, M. B. & Crighton D. G.1976 Physical acoustics and the method of matched asymptotic expansions. In Physical Acoustics, vol. 11 (ed. X. Mason).
Miles J. W.1971 Resonant response of harbours: an equivalent-circuit analysis. J. Fluid Mech. 46, 241–265.Google Scholar
Miles, J. W. & Lee Y. K.1975 Helmholtz resonance of harbours. J. Fluid Mech. 67, 445–464.Google Scholar
Morfey C. L.1969 Acoustic properties of openings at low frequencies. J. Sound Vib. 9, 357–366.Google Scholar
Panton, R. L. & Miller J. M.1975 Resonant frequencies of cylindrical Helmholtz resonators. J. Acoust. Soc. Am. 57, 1533–1535.Google Scholar
Pierce A. D.1981 Acoustics. McGraw-Hill.
Rayleigh Lord1904 On the open organ-pipe problem in two dimensions Phil. Mag. (6) 8, 481–487.Google Scholar
Rayleigh Lord1945 The Theory of Sound, vol. II. Dover.
Ronneberger D.1977 The acoustical impedance of holes in the wall of flow ducts. J. Sound Vib. 24, 133–150.Google Scholar
Tang, P. K. & Sirignano W. A.1973 Theory of a generalized Helmholtz resonator. J. Sound Vib. 26, 247–262.Google Scholar
Walker, B. E. & Charwat A. F.1982 Correlation of the effects of grazing flow on the impedance of Helmholtz resonators. J. Acoust. Soc. Am. 72, 550–555.Google Scholar
Wijngaarden L. Van1968 On the oscillations near and at resonance in open pipes. J. Engng Maths 2, 225–240.Google Scholar