Asymptotic Formulae of the Modal Acoustic Impedance for the Asymmetric Vibrations of a Clamped Circular Plate

• Authors: W. Rdzanek , W. Rdzanek , K. Szemela
• Languages of publication: EN

Abstracts

EN

The asymptotic and approximate formulae for the asymmetric modal acoustic self- and mutual-impedance have been presented for a clamped circular plate embedded into a flat rigid baffle. The formulae have been obtained for the wide frequency band covering the low frequencies, the high frequencies and the middle frequencies. The high frequency asymptotics have been achieved using the method of contour integral and the method of stationary phase. The products of the Bessel and Neumann functions have been expressed as the asymptotic expansions. Further, the approximate formulae valid within the low and middle frequencies have been obtained from the high frequency asymptotics using some mathematical manipulations. The formulae presented are valid for both the axisymmetric vibrations and the asymmetric vibrations.

Keywords

EN

43.20.Ks; 43.20.Rz; 43.40.+s

Discipline

• 43.40.+s: Structural acoustics and vibration

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2010
• Volume: 118
• Issue: 1
• Pages: 141-154

Dates

published

2010-07

Contributors

author

W. Rdzanek

• Department of Acoustics, Institute of Physics, University of Rzeszów, al. Rejtana 16A, 35-310 Rzeszów, Poland

author

W. Rdzanek

• Department of Acoustics, Institute of Physics, University of Rzeszów, al. Rejtana 16A, 35-310 Rzeszów, Poland

author

K. Szemela

• Department of Acoustics, Institute of Physics, University of Rzeszów, al. Rejtana 16A, 35-310 Rzeszów, Poland

References

• 1. A. Berry, J.L. Guyader, J. Nicolas, Journal of the Acoustical Society of America 86, 2792 (1990)
• 2. H. Lee, R. Singh, Noise Control Eng. J. 52 (5), 225 (2004)
• 3. M. Amabili, G. Frosali, M.K. Kwak, Journal of Sound and Vibration 191, 825 (1996)
• 4. J.H. Ginsberg, P. Chu, Journal of the Acoustical Society of America 91, 894 (1992)
• 5. S. Alper, E.B. Magrab, Journal of the Acoustical Society of America 48, 681 (1970)
• 6. X.-F. Wu, A.D. Pierce, J.H. Ginsberg, IEEE Journal of Oceanic Engineering OE-12, 412 (1987)
• 7. H. Lee, R. Singh, Journal of Sound and Vibration 285, 1210 (2005), Short Communication
• 8. Z. Dingguo, M.J. Crocker, Archives of Acoustics 34, 25 (2009)
• 9. Z. Dingguo, M.J. Crocker, Archives of Acoustics 34, 13 (2009)
• 10. H. Levine, F.G. Leppington, Journal of Sound and Vibration 121, 269 (1988)
• 11. C. Kauffmann, Journal of the Acoustical Society of America 104, 3245 (1998)
• 12. L. Shuyu, Acta Acustica united with Acustica 86, 388 (2000)
• 13. W.P. Rdzanek, W. Rdzanek, K. Szemela, Archives of Acoustics 34, 75 (2009)
• 14. W.P. Rdzanek, W. Rdzanek, Z. Engel, K. Szemela, International Journal of Occupational Safety and Ergonomics 13, 147 (2007)
• 15. J.P. Arenas, International Journal of Occupational Safety and Ergonomics 15, 401 (2009)
• 16. W.P. Rdzanek, W.J. Rdzanek, K. Szemela, to be published in Journal of Computational Acoustics
• 17. P. Witkowski, Archives of Acoustics 22, 463 (1997)
• 18. P.M. Morse, K.U. Ingard, Theoretical acoustics, McGraw-Hill, Inc. (1968)
• 19. M. Abramowitz, I.A. Stegun, Ed. Handbook of mathematical functions with formulae, graphs, and mathematical tables, Applied Mathematics Series 55. U.S. Dept. of Commerce, National Bureau of Standards (1972)
• 20. G.N. Watson, A treatise on the theory of Bessel functions, Cambridge University Press (1944)

Identifiers

DOI

10.12693/APhysPolA.118.141