The Radiation Efficiency Measurements of Real System of a Thin Circular Plate Embedded Into a Thick Square Baffle
Abstract
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 platesReferences
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2. 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, https://doi.org/10.1006/jsvi.1996.0158
3. Arenas J.P. (2008), Numerical computation of the sound radiation from a planar baffled vibrating surface, Journal of Computational Acoustics, 16, 3, 321–341, https://doi.org/10.1142/S0218396X08003671
4. Arenas J.P. (2009a), On the sound radiation from a circular hatchway, International Journal of Occupational Safety and Ergonomics, 15, 4, 401–407, https://doi.org/10.1080/10803548.2009.11076819
5. 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.
6. 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.
7. 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.
8. 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, https://doi.org/10.1088/0957-0233/24/12/125101
9. 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.
11. 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, https://doi.org/10.1121/1.4916275
13. 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, https://doi.org/10.1016/j.apacoust.2017.08.020
14. 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, https://doi.org/10.1121/1.4869688
15. 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
16. 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, https://doi.org/10.1016/j.jappmathmech.2017.02.009
17. 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, https://doi.org/10.1260/0263-0923.33.3.371
18. 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, https://doi.org/10.1177/0263092316644085
19. Hashimoto N. (2001), Measurement of sound radiation efficiency by the discrete calculation methods, Applied Acoustics, 62, 429–446, https://doi.org/10.1016/S0003-682X%2800%2900025-6
20. 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, https://doi.org/10.1109/ICMA.2012.6284327
21. Jeong K.-H. (2003), Free vibration of two identical circular plates coupled with bounded fluid, Journal of Sound and Vibration, 260, 4, 653–670, https://doi.org/10.1016/S0022-460X%2802%2901012-X
22. 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, https://doi.org/10.1016/j.jsv.2004.04.029
23. 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, https://doi.org/10.1016/j.apacoust.2016.10.009
24. 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, https://doi.org/10.1016/j.advengsoft.2017.06.001
25. 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, https://doi.org/10.1186/s40712-017-0082-6
26. 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, https://doi.org/10.2478/aoa-2014-0055
27. 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.
28. Kuttruff H. (2007), Acoustics. An Introduction, Taylor and Francis, New York.
29. Kuttruff H. (2009), Room Acoustics, Taylor and Francis, New York.
30. 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, https://doi.org/10.1016/0022-460X%2891%2990696-H
31. 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, https://doi.org/10.1016/j.jsv.2017.12.018
32. 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, https://doi.org/10.1121/1.409993
33. 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
34. Leniowska L. (2006), Effect of active vibration control of a circular plate on sound radiation, Archives of Acoustics, 31, 1, 77–87.
35. Leniowska L., Mazan D. (2015), MFC sensors and actuators in active vibration control of the circular plate, Archives of Acoustics, 40, 2, 257–265, https://doi.org/10.1515/aoa-2015-0028
36. 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
37. 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, https://doi.org/10.1007/s12204-015-1616-9
38. 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.
39. 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, https://doi.org/10.2478/v10168-011-0006-z
40. Mazur K., Pawełczyk M. (2016), Internal model control for a light-weight active noise-reducing casing, Archives of Acoustics, 41, 2, 315–322, https://doi.org/10.1515/aoa-2016-0032
41. Meissner M. (2013), Acoustic behaviour of lightly damped rooms, Acta Acustica united with Acustica, 99, 5, 845–847, https://doi.org/10.3813/AAA.918663
42. 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, https://doi.org/10.1515/aoa-2016-0003
43. 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, https://doi.org/10.1016/j.jsv.2012.11.034
44. 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, https://doi.org/10.1121/1.1908199
45. Rao S.S. (2007), Vibrations of continuous systems, Wiley, New Jersey.
46. Rayleigh J.W.S. (1896), The theory of sound, Vol. 2, Macmillan, New York, 2nd ed.
47. 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, https://doi.org/10.1016/S0022-460X%2802%2901445-1
48. 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, https://doi.org/10.1080/10803548.2007.11076718
49. 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, https://doi.org/10.1142/S0218396X16500181
50. 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, https://doi.org/10.3813/AAA.918934
51. 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, https://doi.org/10.1016/j.camwa.2015.03.022
52. Skudrzyk E. (1971), The Foundations of Acoustics, Basic Mathematics and Basic Acoustics, Springer, New York.
53. 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, https://doi.org/10.1016/j.apacoust.2014.09.013
54. 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
55. 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, https://doi.org/10.1109/JMEMS.2013.2273803
56. Wang X., Xiang Y. (2017), Probes design and experimental measurement of acoustic radiation resistance, International Journal of Acoustics and Vibrations, 22, 2, 252–259, https://doi.org/10.20855/ijav.2017.22.2471
57. 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
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