Archives of Acoustics, 43, 3, pp. 413–423, 2018
10.24425/123913

The Radiation Efficiency Measurements of Real System of a Thin Circular Plate Embedded Into a Thick Square Baffle

Krzysztof SZEMELA
The University of Rzeszów
Poland

Wojciech P. RDZANEK
The University of Rzeszów
Poland

Wojciech ŻYŁKA
The University of Rzeszów
Poland

Most of sound sources are complex vibroacoustic objects consist of numerous elements. Some coupled vibrating plates of different shapes and sizes can be easily found in urban environments. The main aim of this study is to determine the sound radiation of coupled plates system of practical importance. The investigated vibroacoustic system consist of a thin circular plate coupled with a thick flat baffle with a circular hole. The circular plate has been mounted to the baffle’s hole using screws and two steel rings. The measurement setup was located inside a semi-anechoic chamber to assure the free field conditions. It was necessary to take into account the whole system surface to obtain the radiation efficiency based on the Hashimoto’s method. Such an approach can be troublesome and time-consuming. Therefore, the criterion has been proposed which allows the vibration velocity measurements and calculations to be performed only for the thin plate’s area. An alternative approach has been proposed based on the classical Rayleigh integral formula. Its advantage is a simpler implementation in a computer code. The obtained results have been compared with the theoretical results obtained for the elastically supported circular plate. A good agreement has been obtained at low frequencies.
Keywords: radiation efficiency; measurements; Hashimoto’s method; coupled plates
Full Text: PDF
Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).

References

Aarts R.M., Janssen A.J.E.M. (2003), Approximation of the Struve function H1 occurring in impedance calculations, Journal of the Acoustical Society of America, 113, 5, 2635–2637, doi: 10.1121/1.1564019.

Amabili M., Frosali G., Kwak M.K. (1996), Free vibrations of annular plates coupled with fluids, Journal of Sound and Vibration, 191, 5, 825–846, doi: 10.1006/jsvi.1996.0158.

Arenas J.P. (2008), Numerical computation of the sound radiation from a planar baffled vibrating surface, Journal of Computational Acoustics, 16, 3, 321–341, doi: 10.1142/S0218396X08003671.

Arenas J.P. (2009a), On the sound radiation from a circular hatchway, International Journal of Occupational Safety and Ergonomics, 15, 4, 401–407, doi: 10.1080/10803548.2009.11076819.

Arenas J.P. (2009b), Matrix method for estimating the sound power radiated from a vibrating plate for noise control engineering applications, Latin American Applied Research, 39, 4, 345–352.

Arenas J.P. (2010), Calculation of the energy of elastically supported isotropic circular plates at flexural modal vibration frequencies, 17th International Congress on Sound and Vibration 2010, ICSV 2010, 2, 1536–1543.

Arenas J.P., Crocker M.J. (2002), Sound radiation efficiency of a baffled rectangular plate excited by harmonic point forces using its surface resistance matrix, International J. Acoustics and Vibration, 7, 4, 217–229.

Beigelbeck R., Antlinger H., Cerimovic S., Clara S., Keplinger F., Jakoby B. (2013), Resonant pressure wave setup for simultaneous sensing of longitudinal viscosity and sound velocity of liquids, Measurement Science and Technology, 24, 12, 125101, doi: 10.1088/0957-0233/24/12/125101.

Beranek L.L. (1996), Acoustics, Acoustical Society of America, New York. 10. Beranek L.L., Mellow T.J. (2012), Acoustics: sound fields and transducers, Academic Press, New York.

Brański A., Szela S. (2011), Evaluation of the active plate vibration reduction by the parameter of the acoustic field, Acta Physica Polonica A, 119, 6A, 942–945. 12. Chiang H.-Y., Huang Y.-H. (2015), Vibration and sound radiation of an electrostatic speaker based on circular diaphragm, Journal of the Acoustical Society of America, 137, 4, 1714–1721, doi: 10.1121/1.4916275.

Chiang H.-Y., Huang Y.-H. (2018), Resonance mode and sound pressure produced by circular diaphragms of electrostatic and piezoelectric speakers, Applied Acoustics, 129, 365–378, doi: 10.1016/j.apacoust.2017.08.020.

Christiansen T.L., Hansen O., Thomsen E.V., Jensen J.A. (2014), Modal radiation patterns of baffled circular plates and membranes, Journal of the Acoustical Society of America, 135, 5, 2523–2533, doi: 10.1121/1.4869688.

Díaz-Cereceda C., Poblet-Puig J., Rodríguez-Ferran A. (2012), The finite layer method for modelling the sound transmission through double walls, Journal of Sound and Vibration, 331, 22, 4884–4900, doi: https://doi.org/10.1016/j.jsv.2012.06.001.

Gazizullin R.K., Paimushin V.N. (2016), The transmission of an acoustic wave through a rectangular plate between barriers, Journal of Applied Mathematics and Mechanics, 80, 5, 421–432, doi: 10.1016/j.jappmathmech.2017.02.009.

Hasheminejad S., Afsharmanesh B. (2014), Vibroacoustic response of an annular sandwich electrorheological disc, Journal of Low Frequency Noise Vibration and Active Control, 33, 3, 371–394, doi: 10.1260/0263-0923.33.3.371.

Hasheminejad S.M., Keshavarzpour H. (2016), Robust active sound radiation control of a piezo-laminated composite circular plate of arbitrary thickness based on the exact 3d elasticity model, Journal of Low Frequency Noise Vibration and Active Control, 35, 2, 101–127, doi: 10.1177/0263092316644085.

Hashimoto N. (2001), Measurement of sound radiation efficiency by the discrete calculation methods, Applied Acoustics, 62, 429–446, doi: 10.1016/S0003-682X(00)00025-6.

Hu H.H., Shang D.J. (2012), A fast method for the sound radiation of baffled rectangular plate with fluid loading, In 2012 IEEE International Conference on Mechatronics and Automation, pp. 1318–1322, doi: 10.1109/ICMA.2012.6284327.

Jeong K.-H. (2003), Free vibration of two identical circular plates coupled with bounded fluid, Journal of Sound and Vibration, 260, 4, 653–670, doi: 10.1016/S0022-460X(02)01012-X.

Jeong K.-H., Kim K.-J. (2005), Hydroelastic vibration of a circular plate submerged in a bounded compressible fluid, Journal of Sound and Vibration, 283, 1-2, 153–172, doi: 10.1016/j.jsv.2004.04.029.

Jiang C.H., Kam T.Y., Chang Y.H. (2017), Sound radiation of panel-form loudspeaker using flat voice coil for excitation, Applied Acoustics, 116, 375–389, doi: 10.1016/j.apacoust.2016.10.009.

Jung J., Kook J., Goo S., Wang S. (2017), Sound transmission analysis of plate structures using the finite element method and elementary radiator approach with radiator error index, Advances in Engineering Software, 112, 1–15, doi: 10.1016/j.advengsoft.2017.06.001.

Kamper M., Bekker A. (2017), Non-contact experimental methods to characterise the response of a hyper-elastic membrane, International Journal of Mechanical and Materials Engineering, 12, 1, 1–16, doi: 10.1186/s40712-017-0082-6.

Kolber K., Snakowska A., Kozupa M. (2014), The effect of plate discretization on accuracy of the sound radiation efficiency measurements, Archives of Acoustics, 39, 4, 511–518, doi: 10.2478/aoa-2014-0055.

Kozupa M.M., Wiciak J.W. (2011), Comparison of passive and active methods for minimization of sound radiation by vibrating clamped plate, Acta Physica Polonica A, 119, 6 A, 1013–1017.

Kuttruff H. (2007), Acoustics. An Introduction, Taylor and Francis, New York.

Kuttruff H. (2009), Room Acoustics, Taylor and Francis, New York.

Kwak M.K., Kim K.C. (1991), Axisymmetric vibration of circular plates in contact with fluid, Journal of Sound and Vibration, 146, 3, 381–389, doi: 10.1016/0022-460X(91)90696-H.

Langfeldt F., Gleine W., von Estorff O. (2018), An efficient analytical model for baffled, multi-celled membrane-type acoustic metamaterial panels, Journal of Sound and Vibration, 417, 359–375, doi: 10.1016/j.jsv.2017.12.018.

Lee M.-R., Singh R. (1994), Analytical formulations for annular disk sound radiation using structural modes, Journal of the Acoustical Society of America, 95, 6, 3311–3323, doi: 10.1121/1.409993.

Leissa A.W. (1969), Vibration of Plates, Vol. SP-160 of NASA Technical Reports, National Aeronautics and Space Administration, Washington D.C., http://ntrs.nasa.gov/search.jsp?R=19700009156.

Leniowska L. (2006), Effect of active vibration control of a circular plate on sound radiation, Archives of Acoustics, 31, 1, 77–87.

Leniowska L., Mazan D. (2015), MFC sensors and actuators in active vibration control of the circular plate, Archives of Acoustics, 40, 2, 257–265, doi: 10.1515/aoa-2015-0028.

Liu R., Hao Z., Zheng X., Xiong F., Yang W., Jiang J. (2017), The partially-coupled modal contribution assumption of noise radiation and the dominant noise-contribution mode, Journal of Sound and Vibration, 389, 266–275, doi: https://doi.org/10.1016/j.jsv.2016.10.046.

Luo Z., Hao Z.-Y., Zheng X. (2015), Precision improvement of the discrete calculation method for sound radiation research, Journal of Shanghai Jiaotong University (Science), 20, 4, 415–419, doi: 10.1007/s12204-015-1616-9.

Matthews D., Sun H., Saltmarsh K., Wilkes D., Munyard A., Pan J. (2014), A detailed experimental modal analysis of a clamped circular plate, In Iner-Noise 2014, pp. 1–9, Melbourne, Australia, 16–19 November 2014.

Mazur K., Pawełczyk M. (2011), Active noisevibration control using the filtered-reference lms algorithm with compensation of vibrating plate temperature variation, Archives of Acoustics, 36, 1, 65–76, doi: 10.2478/v10168-011-0006-z.

Mazur K., Pawełczyk M. (2016), Internal model control for a light-weight active noise-reducing casing, Archives of Acoustics, 41, 2, 315–322, doi: 10.1515/aoa-2016-0032.

Meissner M. (2013), Acoustic behaviour of lightly damped rooms, Acta Acustica united with Acustica, 99, 5, 845–847, doi: 10.3813/AAA.918663.

Meissner M. (2015), Prediction of reverberant properties of enclosures via a method employing a modal representation of the room impulse response, Archives of Acoustics, 41, 1, doi: 10.1515/aoa-2016-0003.

Oberst S., Lai J.C.S., Marburg S. (2013), Guidelines for numerical vibration and acoustic analysis of disc brake squeal using simple models of brake systems, Journal of Sound and Vibration, 332, 9, 2284–2299, doi: 10.1016/j.jsv.2012.11.034.

Pritchard R.L. (1960), Mutual acoustic impedance between radiators in an infinite rigid plane, Journal of the Acoustical Society of America, 32, 6, 730–737, doi: 10.1121/1.1908199.

Rao S.S. (2007), Vibrations of continuous systems, Wiley, New Jersey.

Rayleigh J.W.S. (1896), The theory of sound, Vol. 2, Macmillan, New York, 2nd ed.

Rdzanek W.P., Engel Z., Rdzanek W.J. (2003), Theoretical analysis of sound radiation of an elastically supported circular plate, Journal of Sound and Vibration, 265, 1, 155–174, doi: 10.1016/S0022-460X(02)01445-1.

Rdzanek W.P., Rdzanek W.J., Engel Z., Szemela K. (2007), The modal low frequency noise of an elastically supported circular plate, International Journal of Occupational Safety and Ergonomics, 13, 2, 147–157, doi: 10.1080/10803548.2007.11076718.

Rdzanek W.P., Rdzanek W.J., Szemela K. (2016), Sound radiation of the resonator in the form of a vibrating circular plate embedded in the outlet of the circular cylindrical cavity, Journal of Computational Acoustics, 24, 4, 1650018, 23 pages, doi: 10.1142/S0218396X16500181.

Robin O., Chazot J.-D., Boulandet R., Michau M., Berry A., Atalla N. (2016), A plane and thin panel with representative simply supported boundary conditions for laboratory vibroacoustic tests, Acta Acustica united with Acustica, 102, 1, 170–182, doi: 10.3813/AAA.918934.

Shahraeeni M., Shakeri R., Hasheminejad S.M. (2015), An analytical solution for free and forced vibration of a piezoelectric laminated plate coupled with an acoustic enclosure, Computers and Mathematics with Applications, 69, 11, 1329–1341, doi: 10.1016/j.camwa.2015.03.022.

Skudrzyk E. (1971), The Foundations of Acoustics, Basic Mathematics and Basic Acoustics, Springer, New York.

Squicciarini G., Putra A., Thompson D.J., Zhang X., Salim M.A. (2015), Use of a reciprocity technique to measure the radiation efficiency of a vibrating structure, Applied Acoustics, 89, 107–121, doi: 10.1016/j.apacoust.2014.09.013.

Sun Y., Pan J., Yang T. (2015), Effect of a fluid layer on the sound radiation of a plate and its active control, Journal of Sound and Vibration, 357, 269–284, doi: https://doi.org/10.1016/j.jsv.2015.07.016.

Vishwakarma S.D., Pandey A.K., Parpia J.M., Southworth D.R., Craighead H.G., Pratap R. (2014), Evaluation of mode dependent fluid damping in a high frequency drumhead microresonator, Journal of Microelectromechanical Systems, 23, 2, 334–346, doi: 10.1109/JMEMS.2013.2273803.

Wang X., Xiang Y. (2017), Probes design and experimental measurement of acoustic radiation resistance, International Journal of Acoustics and Vibrations, 22, 2, 252–259, doi: 10.20855/ijav.2017.22.2471.

Wiciak J. (2007), Modelling of vibration and noise control of a submerged circular plate, Archives of Acoustics, 32, 4S, 265–270, http://acoustics.ippt.pan.pl/index.php/aa/article/view/1419/1236.

Xiaoqing W., Yang X., Zhiyong G., Xuebao X., Yuxiao S., Peng X., Shaowei W. (2014), Research on experimental measurement of acoustic resistance and major accuracy influencing factors analysis, Journal of Mechanical Science and Technology, 28, 4, 1219– 1227, doi: 10.1007/s12206-014-0302-1.

Yuan M., Qiu J., Ji H. (2011), Stiffened panel sound radiation attenuation using acceleration feedback and internal model control, In 2011 Symposium on Piezoelectricity, Acoustic Waves and Device Applications (SPAWDA), pp. 554–557, doi: 10.1109/SPAWDA.2011.6167311.

Yuan M., Ji H., Qiu J., Ma T. (2012), Active control of sound transmission through a stiffened panel using a hybrid control strategy, Journal of Intelligent Material Systems and Structures, 23, 7, 791–803, doi: 10.1177/1045389X12439638.

Zhao J., Qiu J., Ji H. (2016), Reconstruction of the nine stiffness coefficients of composites using a laser generation based imaging method, Composites Science and Technology, 126, 27–34, doi: 10.1016/j.compscitech.2016.02.001.




DOI: 10.24425/123913