Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Archives of Acoustics

The Journal of Institute of Fundamental Technological of Polish Academy of Sciences

4 Issues per year

IMPACT FACTOR 2016: 0.816
5-year IMPACT FACTOR: 0.835

CiteScore 2016: 1.15

SCImago Journal Rank (SJR) 2016: 0.432
Source Normalized Impact per Paper (SNIP) 2016: 0.948

Open Access
See all formats and pricing
More options …
Volume 39, Issue 2


A Numerical Approach to Calculate the Radiation Efficiency of Baffled Planar Structures Using the Far Field

Mario A. González-Montenegro
  • Federal University of Santa Catarina, Department of Mechanical Engineering Campus Trindade, Florianópolis, Brazil
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Roberto Jordan
  • Federal University of Santa Catarina, Department of Mechanical Engineering Campus Trindade, Florianópolis, Brazil
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Arcanjo Lenzi
  • Federal University of Santa Catarina, Department of Mechanical Engineering Campus Trindade, Florianópolis, Brazil
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Jorge P. Arenas
Published Online: 2015-03-01 | DOI: https://doi.org/10.2478/aoa-2014-0029


A numerical method is developed for estimating the acoustic power of any baffled planar structure, which is vibrating with arbitrary surface velocity profile. It is well known that this parameter may be calculated with good accuracy using near field data, in terms of an impedance matrix, which is generated by the discretization of the vibrating surface into a number of elementary radiators. Thus, the sound pressure field on the structure surface can be determined by a combination of the matrix and the volume velocity vector. Then, the sound power can be estimated through integration of the acoustic intensity over a closed surface. On the other hand, few works exist in which the calculation is done in the far field from near field data by the use of radiation matrices, possibly because the numerical integration becomes complicated and expensive due to large variations of directivity of the source. In this work a different approach is used, based in the so-called Propagating Matrix, which is useful for calculating the sound pressure of an arbitrary number of points into free space, and it can be employed to estimate the sound power by integrating over a finite number of pressure points over a hemispherical surface surrounding the vibrating structure. Through numerical analysis, the advantages/disadvantages of the current method are investigated, when compared with numerical methods based on near field data. A flexible rectangular baffled panel is considered, where the normal velocity profile is previously calculated using a commercial finite element software. However, the method can easily be extended to any arbitrary shape. Good results are obtained in the low frequency range showing high computational performance of the method. Moreover, strategies are proposed to improve the performance of the method in terms of both computational cost and speed.

Keywords: propagating matrix; far field; sound power; structural finite element analysis


  • 1. Arenas J.P., Ramis J., Alba J. (2010), Estimation of the sound pressure field of a baffled uniform elliptically shaped transducer, Appl. Acoust., 71, 128-133.Web of ScienceGoogle Scholar

  • 2. Atalla N., Nicolas J. (1994), A new tool for predicting rapidly and rigorously the radiation efficiency of plate-like structures, J. Acoust. Soc. Am., 95, 3369-Google Scholar

  • 3378.Google Scholar

  • 3. Bai M.R., Tsao M. (2002), Estimation of sound power of baffled planar sources using radiation matrices, J. Acoust. Soc. Am., 112, 876-883.Google Scholar

  • 4. Baumann W.T., Ho F.-S., Robertshaw H.H. (1992), Active structural acoustic control of broadband disturbances, J. Acoust. Soc. Am., 92, 1998-2005.Google Scholar

  • 5. Berkhoff A.P. (2002), Broadband radiation modes: Estimation and active control, J. Acoust. Soc. Am., 111, 1295-1305.Google Scholar

  • 6. Berry A. (1991), Vibration and acoustic radiation of planar structures, complex immersed in a light fluid or in a heavy fluid, [in French: Vibrations et rayonnement acoustique de structures planes, complexes immergées dans un fluide léger ou dans un fluide lourd], Université de Sherbrooke, Ph.D. Thesis.Google Scholar

  • 7. Borgiotti G.V. (1990), The power radiated by a vibrating body in an acoustic fluid and its determination from boundary measurements, J. Acoust. Soc. Am., 88, 1884-1893.Google Scholar

  • 8. Borgiotti G.V., Jones K.E. (1994), Frequency independence property of radiation spatial filters, J. Acoust. Soc. Am., 96, 3516-3524.Google Scholar

  • 9. Cremer L., Heckl M., Ungar E.E. (1988), Structure-Borne Sound, Springer-Verlag, Berlin.Google Scholar

  • 10. Cunefare K.A., Koopmann G.H. (1991), Global optimum active noise control: Surface and far-field effects, J. Acoust. Soc. Am., 90, 365-373.Google Scholar

  • 11. Elliot S.J., Johnson M.E. (1993), Radiation modes and the active control of sound power, J. Acoust. Soc. Am., 94, 2194-2204.Google Scholar

  • 12. Fahy F.J., Gardonio P. (2007), Sound and Structural Vibration, Academic Press, Oxford.Google Scholar

  • 13. Fan X., Moros E., Straube W.L. (1997), Acoustic field prediction for a single planar continuouswave source using an equivalent phased array method, J. Acoust. Soc. Am., 102, 2734-2741.Google Scholar

  • 14. Fiates F. (2003), Sound radiation of beam-reinforced plates, [in Portuguese: Radicao sonora de placas refocadas por vigas], Universidade Federal de Santa Catarina, Ph.D. Thesis.Google Scholar

  • 15. Fisher J.M., Blotter J.D., Somerfeldt S.D., Gee K.L. (2012), Development of a pseudo-uniform structural quantity for use in active structural acoustic control of simply supported plates: An analytical comparison, J. Acoust. Soc. Am., 131, 3833-3840.Web of ScienceGoogle Scholar

  • 16. ISO-3745 (2003), Acoustics - Determination of sound power levels of noise sources - Precision methods for anechoic and semi-anechoic rooms, Geneva, Switzerland: ISO.Google Scholar

  • 17. Langley R.S. (2007), Numerical evaluation of the acoustic radiation from planar structures with general baffle conditions using wavelets, J. Acoust. Soc. Am., 121, 766-777.Web of ScienceGoogle Scholar

  • 18. Li W.L. (2006), Vibroacoustic analysis of rectangular plates with elastic rotational edge restraints, J. Acoust. Soc. Am., 120, 769-779.Google Scholar

  • 19. Maidanik G. (1962), Response of Ribbed Panels to Reverberant Acoustic Fields, J. Acoust. Soc. Am., 34, 809-826.Google Scholar

  • 20. Mollo C.G., Bernhard R.J. (1989), Generalised method of predicting optimal performance of active noise controllers, J. AIAA, 27, 1473-1478.Google Scholar

  • 21. Naghshineh K., Koopmann G.H., Belegundu A.D. (1992), Material tailoring of structures to achieve a minimum radiation condition, J. Acoust. Soc. Am., 92, 841-855.Google Scholar

  • 22. Naghshineh K., Koopmann G.H. (1993), Active control of sound power using acoustic basis functions as surface velocity filters, J. Acoust. Soc. Am., 93, 2740-Google Scholar

  • 2752.Google Scholar

  • 23. Pàmies T., Romeu J., Genescà M., Balastegui A. (2011), Sound radiation from an aperture in a rectangular enclosure under low modal conditions, J. Acoust. Soc. Am., 130, 239-248.Web of ScienceGoogle Scholar

  • 24. Rayleigh L. (1896), The Theory of Sound, Dover, 130, New York.Google Scholar

  • 25. Sandman B.E. (1977), Fluid-loaded vibration of an elastic plate carrying a concentrated mass, J. Acoust. Soc. Am., 61, 1503-1510.Google Scholar

  • 26. Wallace C.E. (1972), Radiation resistance of a rectangular panel, J. Acoust. Soc. Am., 51, 946-952.Google Scholar

  • 27. Williams E.G., Maynard J.D. (1982), Numerical evaluation of the Rayleigh integral for planar radiators using the FFT, J. Acoust. Soc. Am., 72, 2020-2030.Google Scholar

  • 28. Zou D., Crocker M.J. (2009), Sound Power Radiated from Rectangular Plates, Arch. Acoust., 34, 1, 25-39.Google Scholar

About the article

Received: 2013-05-20

Accepted: 2014-06-04

Published Online: 2015-03-01

Citation Information: Archives of Acoustics, Volume 39, Issue 2, Pages 249–260, ISSN (Online) 2300-262X, DOI: https://doi.org/10.2478/aoa-2014-0029.

Export Citation

© 2014 Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN). This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

W.P. Rdzanek
Acta Physica Polonica A, 2015, Volume 128, Number 1A, Page A-41

Comments (0)

Please log in or register to comment.
Log in