Archives of Acoustics, 39, 2, pp. 249-260, 2014
10.2478/aoa-2014-0029

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

Mario A. GONZÁLEZ-MONTENEGRO
Institute of Acoustics, Univ. Austral de Chile, PO Box 567, Valdivia.
Chile

Roberto JORDAN
Federal University of Santa Catarina, Department of Mechanical Engineering, Campus Trindade, Florianópolis.
Brazil

Arcanjo LENZI
Federal University of Santa Catarina, Department of Mechanical Engineering, Campus Trindade, Florianópolis.
Brazil

Jorge P. ARENAS
Institute of Acoustics, Univ. Austral de Chile, PO Box 567, Valdivia.
Chile

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.
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References

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.

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--3378.

BAI M.R., TSAO M. (2002). Estimation of sound power of baffled planar sources using radiation matrices, J Acoust Soc Am, 112, 876--883.

BAUMANN W.T., HO F.-S., ROBERTSHAW H.H. (1992). Active structural

acoustic control of broadband disturbances, J Acoust Soc Am, 92, 1998--2005.

BERKHOFF A.P. (2002). Broadband radiation modes: Estimation and active control, J Acoust Soc Am, 111, 1295--1305.

BERRY A. (1991), Vibration and acoustic radiation of planar structures,

complex immersed in a light fluid or in a heavy fluid}, Université de Sherbrooke, Ph.D. Thesis.

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.

BORGIOTTI G.V., JONES K.E. (1994). Frequency independence property of

radiation spatial filters, J Acoust Soc Am, 96, 3516--3524.

CREMER L., HECKL M., UNGAR E.E. (1988). Structure-Borne Sound, Springer-Verlag, Berlin.

CUNEFARE K.A., KOOPMANN G.H. (1991). Global optimum active noise control: Surface and far-field effects, J Acoust Soc Am, 90, 365--373.

ELLIOT S.J., JOHNSON M.E. (1993). Radiation modes and the active control of sound power, J Acoust Soc Am, 94, 2194--2204.

FAHY F.J., GARDONIO P. (2007). Sound and Structural Vibration, Academic Press, Oxford.

FAN X., MOROS E., STRAUBE W.L. (1997). Acoustic field prediction for a single planar continuous-wave source using an equivalent phased array method, J Acoust Soc Am, 102, 2734--2741.

FIATES F. (2003), Sound radiation of beam-reinforced plates, Universidade Federal de Santa Catarina, Ph.D. Thesis.

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.

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

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.

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

MAIDANIK G. (1962). Response of Ribbed Panels to Reverberant Acoustic Fields, J Acoust Soc Am, 34, 809--826.

MOLLO C.G., BERNHARD R.J. (1989). Generalised method of predicting optimal performance of active noise controllers, J AIAA, 27, 1473--1478.

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.

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--2752.

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.

RAYLEIGH L. (1896). The Theory of Sound, Dover, 130, New York.

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

WALLACE C.E. (1972). Radiation resistance of a rectangular panel, J Acoust Soc Am, 51, 946--952.

WILLIAMS E., MAYNARD J. (1982). Numerical evaluation of the Rayleigh integral for planar radiators using the FFT, J Acoust Soc Am, 72, 2020--2030.

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.

ZOU D., CROCKER M.J. (2009). Sound Power Radiated from Rectangular Plates, Arch Acoust, 34,1, 25--39.




DOI: 10.2478/aoa-2014-0029

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