A comparison of time domain boundary conditions for acoustic waves in wave guides
Authors:
H. T. Banks, G. Propst and R. J. Silcox
Journal:
Quart. Appl. Math. 54 (1996), 249-265
MSC:
Primary 76Q05; Secondary 35L05, 35Q99, 35R30
DOI:
https://doi.org/10.1090/qam/1388015
MathSciNet review:
MR1388015
Full-text PDF Free Access
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Abstract: We consider several types of boundary conditions in the context of time domain models for acoustic waves. Experiments with four different duct terminations (hardwall, free radiation, foam, wedge) were carried out in a wave duct from which reflection coefficients over a wide frequency range were measured. These reflection coefficients are used to estimate parameters in the time domain boundary conditions, and a comparison of the relative merits of the models in describing the data is presented. Boundary conditions that yield a good fit of the model to the experimental data were found for all duct terminations except the wedge.
P. M. Morse and K. U. Ingard, Theoretical Acoustics, McGraw-Hill, New York, 1968
W. E. Zorunski and T. L. Parrott, Non-linear acoustic theory for rigid porous materials, NASA TN D-6196, June 1971
S. I. Hariharan and H. C. Lester, A finite difference solution for the propagation of sound in near sonic flows, J. Acoust. Soc. Amer. 75, 1052 1061 (1984)
J. S. Preisser, et al, Flight study of induced Turbofan inlet radiation with theoretical comparisons, AIAA J. of Aircraft 22, 57 62 (1985)
W. R. Watson and M. K. Myers, Numerical computation of steady state acoustic disturbances in flow, AIAA paper no. AIAA-92-02-074 presented at DGLR/AIAA 14th Aeroacoustics Conference, Aachen, FRG, May 11–14, 1992
K. R. Meadows and J. C. Hardin, Removal of spurious reflections from computational fluid dynamic solutions with the complex Cepstrum, AIAA Journal 30, 29–34 (1992)
B. Bolton and E. Gold, The determination of acoustic reflection coefficients by using spectral techniques, I: Experimental procedures and measurements of polyurethane foam, J. Sound Vibration 110, no. (2), 179–202 (1986)
J. T. Beale, Spectral properties of an acoustic boundary condition, Indiana Univ. Math. J. 25, 895–917 (1976)
J. T. Beale and S. I. Rosencrans, Acoustic boundary conditions, Bull. Amer. Math. Soc. (N.S.) 80, 1276–1278 (1974)
A. Majda, Disappearing solutions for the dissipative wave equation, Indiana Univ. Math. J. 24, 1119–1133 (1975)
G. Chen, A note on the boundary stabilization of the wave equation, SIAM J. Control Optimization 19, 106–113 (1981)
H. T. Banks, S. L. Keeling, and R. J. Silcox, Optimal control techniques for active noise suppression, Proc. 27th Conf. on Decision and Control, Austin, TX, 1988, pp. 2006–2011
A. Majda, The location of the spectrum for the dissipative acoustic operator, Indiana Univ. Math. J. 25, 973–987 (1976)
J. Lagnese, Decay of solutions of wave equations in a bounded region with boundary dissipation, J. Differential Equations 50, 163–182 (1983)
D. L. Russell, Control theory of hyperbolic equations related to certain questions in harmonic analysis and spectral theory, J. Math. Anal. Appl. 40, 336–368 (1972)
H. T. Banks, G. Propst, and R. J. Silcox, Groups generated by wave-duct acoustics with impedance boundary conditions, CAMS Tech. Report #90-10, University of Southern California, August, 1990
M. G. Jones and T. L. Parrott, Evaluation of a multi-point method for determining acoustic impedance, Mechanical Systems and Signal Processing 3, no. (1), 15–35 (1989)
B. S. Garbow, K. E. Hillstrom, and J. J. More, Documentation for MINPACK subroutine LMDIF1, Argonne National Laboratory, 1980
P. M. Morse and K. U. Ingard, Theoretical Acoustics, McGraw-Hill, New York, 1968
W. E. Zorunski and T. L. Parrott, Non-linear acoustic theory for rigid porous materials, NASA TN D-6196, June 1971
S. I. Hariharan and H. C. Lester, A finite difference solution for the propagation of sound in near sonic flows, J. Acoust. Soc. Amer. 75, 1052 1061 (1984)
J. S. Preisser, et al, Flight study of induced Turbofan inlet radiation with theoretical comparisons, AIAA J. of Aircraft 22, 57 62 (1985)
W. R. Watson and M. K. Myers, Numerical computation of steady state acoustic disturbances in flow, AIAA paper no. AIAA-92-02-074 presented at DGLR/AIAA 14th Aeroacoustics Conference, Aachen, FRG, May 11–14, 1992
K. R. Meadows and J. C. Hardin, Removal of spurious reflections from computational fluid dynamic solutions with the complex Cepstrum, AIAA Journal 30, 29–34 (1992)
B. Bolton and E. Gold, The determination of acoustic reflection coefficients by using spectral techniques, I: Experimental procedures and measurements of polyurethane foam, J. Sound Vibration 110, no. (2), 179–202 (1986)
J. T. Beale, Spectral properties of an acoustic boundary condition, Indiana Univ. Math. J. 25, 895–917 (1976)
J. T. Beale and S. I. Rosencrans, Acoustic boundary conditions, Bull. Amer. Math. Soc. (N.S.) 80, 1276–1278 (1974)
A. Majda, Disappearing solutions for the dissipative wave equation, Indiana Univ. Math. J. 24, 1119–1133 (1975)
G. Chen, A note on the boundary stabilization of the wave equation, SIAM J. Control Optimization 19, 106–113 (1981)
H. T. Banks, S. L. Keeling, and R. J. Silcox, Optimal control techniques for active noise suppression, Proc. 27th Conf. on Decision and Control, Austin, TX, 1988, pp. 2006–2011
A. Majda, The location of the spectrum for the dissipative acoustic operator, Indiana Univ. Math. J. 25, 973–987 (1976)
J. Lagnese, Decay of solutions of wave equations in a bounded region with boundary dissipation, J. Differential Equations 50, 163–182 (1983)
D. L. Russell, Control theory of hyperbolic equations related to certain questions in harmonic analysis and spectral theory, J. Math. Anal. Appl. 40, 336–368 (1972)
H. T. Banks, G. Propst, and R. J. Silcox, Groups generated by wave-duct acoustics with impedance boundary conditions, CAMS Tech. Report #90-10, University of Southern California, August, 1990
M. G. Jones and T. L. Parrott, Evaluation of a multi-point method for determining acoustic impedance, Mechanical Systems and Signal Processing 3, no. (1), 15–35 (1989)
B. S. Garbow, K. E. Hillstrom, and J. J. More, Documentation for MINPACK subroutine LMDIF1, Argonne National Laboratory, 1980
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Article copyright:
© Copyright 1996
American Mathematical Society
