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The damping of flexural and acoustic waves by a bias-flow perforated elastic plate

Published online by Cambridge University Press:  26 September 2008

M. S. Howe
M. S. Howe
Affiliation:
College of Engineering, Boston University, 110 Cummington Street, Boston, MA 02215, USA
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Abstract

An analysis is made of the damping of sound and structural vibrations by vorticity production in the apertures of a bias flow, perforated elastic plate. Unsteady motion causes vorticity to be generated at the aperture edges; the vorticity and its energy are swept away by the bias flow and result in a net loss of acoustic and vibrational energy. In this paper we investigate the interaction of an arbitrary fluid-structure disturbance with a small circular aperture in the presence of a high Reynolds number, low Mach number bias flow. By considering the limit in which the aperture is small compared to the length scale of the impinging disturbance, it is shown that the effect of the interaction can be represented by a concentrated source in the plate bending wave equation consisting of a delta function and two of its axisymmetric derivatives. A generalized bending wave equation is then formulated for a plate perforated with an homogeneous distribution of small, bias flow circular apertures. This equation is used to predict the attenuation of sound and resonant bending waves by vorticity production. Acoustic damping is found to be significant provided the fluid loading is sufficiently small for the plate to be regarded as rigid (e.g. for an aluminium plate in air when the frequency is not too small). On the other hand, a bending wave is effectively damped only when the fluid loading is large enough for the wave to produce a substantial pressure drop across the plate; when this occurs the predicted attenuations are comparable with those usually achieved by the application of elastomeric damping materials. Numerical predictions are presented for steel and aluminium plates in air and water.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 6 , Issue 4 , August 1995 , pp. 307 - 328
Copyright
Copyright © Cambridge University Press 1995

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References

[1]Lighthill, M. J. 1952 On sound generated aerodynamically. Part I: General theory. Proc. Roy. Soc. Lond. A 211, 564–587.Google Scholar
[2]Curle, N. 1955 The influence of solid boundaries upon aerodynamic sound. Proc. Roy. Soc. Lond. A 231, 505–514.Google Scholar
[3]Powell, A. 1963 Mechanisms of aerodynamic sound production. AGARD Rept. 466.Google Scholar
[4]Ffowcs Williams, J. E. & Hawkings, D. L. 1969 Sound generation by turbulence and surfaces in arbitrary motion. Phil. Trans. Roy. Soc. A 264, 321–342.Google Scholar
[5]Howe, M. S. 1975 Contributions to the theory of aerodynamic sound, with application to excess jet noise and the theory of the flute. J. Fluid Mech. 71, 625–673.CrossRefGoogle Scholar
[6]Crighton, D. G. 1981 Acoustics as a branch of fluid mechanics. J. Fluid Mech. 106, 261–298.CrossRefGoogle Scholar
[7]Lilley, G. M. 1991 Jet noise classical theory and experiments. In Hubbard, H. H. (ed.), Aeroacoustic of Flight Vehicles: Theory and Practice. Volume I: Noise Source. NASA Ref. Publ. 1258.Google Scholar
[8]Ffowcs Williams, J. E. 1965 Sound radiation from turbulent boundary layers formed on compliant surfaces. J. Fluid Mech. 22, 347–358.CrossRefGoogle Scholar
[9]Chandiramani, K. L. 1977 Vibration response of fluid loaded structures to low speed flow noise. J. Acoust. Soc. Am. 61, 1460–1470.CrossRefGoogle Scholar
[10]Blake, W. K. 1986 Mechanics of flow-induced sound and vibration, Vol. 2: Complex flow-structure interactions. Academic Press.Google Scholar
[11]Howe, M. S. 1993 Structural and acoustic noise produced by turbulent flow over an elastic trailing edge. Proc. Roy. Soc. Lond. A 442, 533–554.Google Scholar
[12]Rienstra, S. W. 1981 Sound diffraction at a trailing edge. J. Fluid Mech. 108, 443–460.CrossRefGoogle Scholar
[13]Howe, M. S. 1984 On the absorption of sound by turbulence and other hydrodynamic flows. IMA J. Appl. Math. 32, 187–209.CrossRefGoogle Scholar
[14]Ver, I. L. 1982 Perforated baffles prevent flow-induced acoustic resonances in heat exchangers. Meeting of the Federation of the Acoustical Societies of Europe,Gottingen,September.Google Scholar
[15]Ver, I. L. 1990 Practical examples of noise and vibration control: case history of consulting projects. Noise Control Eng. J. 35, 115–125.CrossRefGoogle Scholar
[16]Bloxsidge, G. J., Dowling, A. P. & Langhorne, P. J. 1988 Reheat buzz: an acoustically coupled combustion instability. Part 2. Theory. J. Fluid Mech. 193, 445–473.CrossRefGoogle Scholar
[17]Hughes, I. J. & Dowling, A. P. 1990 The absorption of sound by perforated linings. J. Fluid Mech. 218, 299–336.CrossRefGoogle Scholar
[18]Bechert, D., Michel, U. & Pfizenmaier, E. 1977 Experiments on the transmission of sound through jets. AIAA Paper 77–1278.Google Scholar
[19]Bechert, D. W. 1979 Sound absorption caused by vorticity shedding, demonstrated with a jet flow. AIAA Paper 79–0575.Google Scholar
[20]Howe, M. S. 1980 The dissipation of sound at an edge. J. Sound Vib. 70, 407–411.CrossRefGoogle Scholar
[21]Howe, M. S. 1979 On the theory of unsteady high Reynolds number flow through a circular aperture. Proc. Roy. Soc. Lond. A 366, 205–233.Google Scholar
[22]Howe, M. S. 1980 On the diffraction of sound by a screen with circular apertures in the presence of a low Mach number grazing flow. Proc. Roy. Soc. Lond. A 370, 523–544.Google Scholar
[23]Fukumoto, Y. & Takayama, M. 1991 Vorticity production at the edge of a slit by sound waves in the presence of a low Mach number bias flow. Phys. Fluids A 3, 3080–3082.CrossRefGoogle Scholar
[24]Dowling, A. P. & Hughes, I. J. 1992 Sound absorption by a screen with a regular array of slits. J. Sound Vib. 156, 387–405.CrossRefGoogle Scholar
[25]Cargill, A. M. 1982 Low frequency sound radiation and generation due to the interaction of unsteady flow with a jet pipe. J. Fluid Mech. 121, 59–105.CrossRefGoogle Scholar
[26]Blackman, A. W. 1960 Effect of nonlinear losses on the design of absorbers for combustion instabilities. Am. J. Rocket Soc. November 1022–1028.Google Scholar
[27]Zinn, B. T. 1970 A theoretical study of nonlinear damping by Helmholtz resonators. J. Sound Vib. 13, 347–356.CrossRefGoogle Scholar
[28]Melling, T. H. 1973 The acoustic impedance of perforates at medium and high sound pressure levels. J. Sound Vib. 29, 1–65.CrossRefGoogle Scholar
[29]Cummings, A. 1983 Acoustic nonlinearities and power losses at orifices. AIAA Paper 83–0739.Google Scholar
[30]Cummings, A. 1984 Transient and multiple frequency sound transmission through perforated plates at high amplitude. AIAA Paper 84–2311.Google Scholar
[31]Howe, M. S. 1992 On the damping of structural vibrations by vortex shedding. J.d' Acoustique 5, 603–620.Google Scholar
[32]Beranek, L. L. & Ver, I. L. 1992 Noise and Vibration Control Engineering. Wiley.Google Scholar
[33]Cremer, L., Heckl, M. & Ungar, E. E. 1988 Structure-Borne Sound (2nd ed.). Springer-Verlag.CrossRefGoogle Scholar
[34]Kraus, H. 1967 Thin Elastic Shells. Wiley.Google Scholar
[35]Gel'Fand, I. M. & Shilov, G. E. 1964 Generalized Functions. Volume 2: Spaces of Fundamental and Generalized Functions. Academic Press.Google Scholar
[36]Lighthill, M. J. 1960 Studies on magneto-hydrodynamic waves and other anisotropic wave motions. Phil. Trans. Roy. Soc. A 252, 397–430.Google Scholar
[37]Abramowitz, M. & Stegun, I. A. (eds) 1970 Handbook of Mathematical Functions (Ninth corrected printing), US Dept. of Commerce, Nat. Bur. Stands. Appl. Math. Ser. No. 55.Google Scholar
[38]Rayleigh, Lord 1945 Theory of Sound, Vol. 2. Dover.Google Scholar
[39]Howe, M.S. 1992 Sound produced by an aerodynamic source adjacent to a partly coated, finite elastic plate. Proc. Roy. Soc. Lond. A 436, 351–372.Google Scholar
[40]Williams, F. A. 1985 Combustion Theory (2nd ed.). Benjamin/Cummings.Google Scholar
[41]Marble, F. E. 1970 Dynamics of dusty gases. Ann. Rev. Fluid Mech. 2, 397–446.CrossRefGoogle Scholar
[42]Marble, F. E. & Wooton, D. C. 1970 Sound attenuation in condensing vapor. Phys. Fluids 13, 2657–2664.CrossRefGoogle Scholar
[43]Marble, F. E. 1975 Acoustic attenuation by vaporization of liquid droplets - application to noise reduction in aircraft power plants. Cal. Tech. Guggenheim Jet Propulsion Center Rept. AFOSR-TR 75–0511.Google Scholar
[44]Wijngaarden, L. Van 1979 Sound and shock waves in bubbly liquids. In Lauterborn, W. (ed.), Caviatation and Inhomogeneities in Underwater Acoustics. Springer-Verlag.Google Scholar
[45]Wijngaarden, L. Van & Kapteyn, C. 1990 Concentration waves in dilute bubble/liquid mixtures. J. Fluid Mech. 212, 111–138.CrossRefGoogle Scholar
[46]Brillouin, L. 1960 Wave Propagation and Group Velocity. Academic Press.Google Scholar
[47]Tolstoy, I. 1983 Coherent modes and boundary waves in a rough-walled acoustic waveguide. J. Acoust. Soc. Am. 73, 1192–1199.CrossRefGoogle Scholar
[48]Tolstoy, I. 1985 Rough surface boundary wave attenuation due to incoherent scatter. J. Acoust. Soc. Am. 77, 482–488.CrossRefGoogle Scholar