Effect of Acoustic Enclosure on the Sound Transmission Loss of Multi-Layered Micro-Perforated Plates
Abstract
This study presents an examination of the transmission properties of multilayered partitions made up of multiple micro-perforated plates (MPPs) coupled to acoustic enclosures with general impedance boundaries. Multi-layered MPPs can lower the transmission while minimizing reflection in the source and receiving enclosure. Previous research has mainly focused on the double MPPs or triple MPPs partition itself. However, it is vital to analyze the in-situ sound transmission loss of the multi-layered MPP and their efficiency in a complex vibro-acoustic environment. The case when the multilayered MPPs are coupled to a receiving enclosure or coupled to both a source and receiving enclosure is investigated. The objective is to provide an analytical method to evaluate the transmission properties of multilayered MPPs coupled to acoustic enclosures while being computationally more efficient than the finite element method (FEM). Using the modified Fourier series for the acoustic pressure, a variational form for the acoustic and structure medium yields a completely coupled vibroacoustic system. A comparison between the sound transmission loss of the double MPPs, when mounted on an impedance tube and coupled to acoustics enclosures, shows the modal effect of the enclosures. The effect of enclosure shape, impedance boundary, perforation ratio, air gap thickness on the sound transmission properties of the double MPPs structure is examined for both cases. Finally, in both situations, the performance of triple MPP structure insulation is evaluated.Keywords:
micro-perforated plate (MPP), sound transmission loss, noise insulation, coupled structuralacoustic, surface impedance, modal analysisReferences
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7. Bravo T., Maury C., Pinhède C. (2016), Optimisation of micro-perforated cylindrical silencers in linear and nonlinear regimes, Journal of Sound and Vibration, 363: 359–379, https://doi.org/10.1016/j.jsv.2015.11.011
8. Carneal J.P., Fuller C.R. (2004), An analytical and experimental investigation of active structural acoustic control of noise transmission through double panel system, Journal of Sound and Vibration, 272(3–5): 749–771, https://doi.org/10.1016/S0022-460X%2803%2900418-8
9. Chazot J.-D., Guyader J.-L. (2007), Prediction of transmission loss of double panels with a patch-mobility method, The Journal of the Acoustical Society of America, 121(1): 267–78, https://doi.org/10.1121/1.2395920
10. Cheng L., Li Y.Y., Gao J.X. (2005), Energy transmission in a mechanically-linked double-wall structure coupled to an acoustic enclosure, The Journal of the Acoustical Society of America, 117(5): 2742–2751, https://doi.org/10.1121/1.1886525
11. Chien W.Z. (1983), Method of high-order Lagrange multiplier and generalized variational principles of elasticity with more general forms of functional, Applied Mathematics and Mechanics, 4: 143–157, https://doi.org/10.1007/BF01895439
12. Delany M.E., Bazley E.N. (1970), Acoustical properties of fibrous materials, Applied Acoustics, 3(2): 105–116, https://doi.org/10.1016/0003-682X%2870%2990031-9
13. Du J.T., Li W.L., Liu Z.G., Xu H.A., Ji Z.L. (2011), Acoustic analysis of a rectangular cavity with general impedance boundary condition, The Journal of the Acoustical Society of America, 130(9): 807–817, https://doi.org/10.1121/1.3605534
14. Dupont T., Pavic G., Laulagnet B. (2003), Acoustic properties of lightweight micro-perforated plate systems, Acta Acustica united Acustica, 89(2): 201–212.
15. Falsafi I., Ohadi A. (2018), Optimisation of multistep cavity configuration to extend absorption bandwidth of micro perforated panel absorber, Archives of Acoustics, 43(2): 187–195, https://doi.org/10.24425/122366
16. Fuchs H.V., Zha X. (1997), Acrylic-glass sound absorbers in the plenum of the deutscher bundestag, Applied Acoustics, 51(2): 211–217, https://doi.org/10.1016/S0003-682X%2896%2900064-3
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18. Kang J., Brocklesby M.W. (2005), Feasibility of applying micro-perforated absorbers in acoustic window systems, Applied Acoustics, 66(6): 669–689, https://doi.org/10.1016/j.apacoust.2004.06.011
19. Kihlman T. (1967), Sound radiation into a rectangular room. Applications to airborne sound transmission in buildings, Acta Acustica, 18(1): 11–20.
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22. Kropp W., Pietrzyk A., Kihlman T. (1994), On the meaning of the sound reduction index at low frequencies, Acta Acustica (Les Ulis), 2(5): 379–392.
23. Liu Z., Zhan J., Fard M., Davy J.L. (2017), Acoustic properties of multilayer sound absorbers with a 3D printed micro-perforated panel, Applied Acoustics, 121: 25–32, https://doi.org/10.1016/j.apacoust.2017.01.032
24. Løvholt F., Norèn-Cosgriff K., Madshus C., Ellingsen S.E. (2017), Simulating low frequency sound transmission through walls and windows by a two-way coupled fluid structure interaction model, Journal of Sound and Vibration, 396: 203–216, https://doi.org/10.1016/j.jsv.2017.02.026
25. Maa D.-Y. (1998), Potential of microperforated panel absorber, The Journal of the Acoustical Society of America, 104(5): 2861–2866, https://doi.org/10.1121/1.423870
26. Meng H., Galland M.A., Ichchou M., Bareille O., Xin F.X., Lu T.J. (2017), Small perforations in corrugated sandwich panel significantly enhance low-frequency sound absorption and transmission loss, Composite Structures, 182: 1–11, https://doi.org/10.1016/j.compstruct.2017.08.103
27. Meng H., Galland M.A., Ichchou M., Xin F.X., Lu T.J. (2019), On the low-frequency acoustic properties of novel multifunctional honeycomb sandwich panels with micro-perforated faceplates, Applied Acoustics, 152: 31–40, https://doi.org/10.1016/j.apacoust.2019.02.028
28. Mu R.L., Toyoda M., Takahashi D. (2011a), Improvement of sound insulation performance of multilayer windows by using microperforated panel, Acoustical Science and Technology, 32(2): 79–81, https://doi.org/10.1250/ast.32.79
29. Mu R. L., Toyoda M., Takahashi D. (2011b), Sound insulation characteristics of multi-layer structures with a microperforated panel, Applied Acoustics, 72(11): 849–855, https://doi.org/10.1016/j.apacoust.2011.05.009
30. Mulholland K.A., Lyon R.H. (1973), Sound insulation at low frequencies, The Journal of the Acoustical Society of America, 54(4): 867–878, https://doi.org/10.1121/1.1914340
31. Osipov A., Mees P., Vermeir G. (1997a), Numerical simulations of airborne sound transmission at low frequencies: The influence of the room and the partition parameters, [in:] Proceedings of InterNoise 97, pp. 759–762.
32. Osipov A., Mees P., Vermeir G. (1997b), Low-frequency airborne sound transmission through single partitions in buildings, Applied Acoustics, 52(3–4): 273–288, https://doi.org/10.1016/S0003-682X%2897%2900031-5
33. Pfretzschner J., Cobo P., Simón F., Cuesta M., Fernández A. (2006), Microperforated insertion units: An alternative strategy to design microperforated panels, Applied Acoustics, 67(1): 62–73, https://doi.org/10.1016/j.apacoust.2005.05.005
34. Qu Y.G., Hua H.X., Meng G. (2013a), A domain decomposition approach for vibration analysis of isotropic and composite cylindrical shells with arbitrary boundaries, Composite Structures, 95: 307–321, https://doi.org/10.1016/j.compstruct.2012.06.022
35. Qu Y.G., Chen Y., Long X.H., Hua H.X., Meng G. (2013b), A modified variational approach for vibration analysis of ring-stiffened conical–cylindrical shell combinations, European Journal of Mechanics – A/Solids, 37: 200–215, https://doi.org/10.1016/j.euromechsol.2012.06.006
36. Takahashi D., Tanaka M. (2002), Flexural vibration of perforated plates and porous elastic materials under acoustic loading, Journal of the Acoustical Society of America, 112(4): 1456-1464, https://doi.org/10.1121/1.1497624
37. Tang Y., Xin F., Huang L., Lu T.J. (2017), Deep subwavelength acoustic metamaterial for low-frequency sound absorption, Europhysics Letters, 118(4): 44002, https://doi.org/10.1209/0295-5075/118/44002
38. Tang Y., Xin F., Huang L., Lu T.J. (2019), Sound absorption of micro-perforated sandwich panel with honeycomb-corrugation hybrid core at high temperatures, Composite Structures, 226: 111285, https://doi.org/10.1016/j.compstruct.2019.111285
39. Toyoda M., Takahashi D. (2008), Sound transmission through a microperforated-panel structure with subdivided air cavities, The Journal of the Acoustical Society of America, 124(6): 3594–3603, https://doi.org/10.1121/1.3001711
40. Xin F.X., Lu T.J., Chen C.Q. (2008), Vibroacoustic behavior of clamp mounted double-panel partition with enclosure air cavity, The Journal of the Acoustical Society of America, 124(6): 3604–3612, https://doi.org/10.1121/1.3006956
41. Yang C., Cheng L. (2016), Sound absorption of microperforated panels inside compact acoustic enclosures, Journal of Sound and Vibration, 360: 140–155, https://doi.org/10.1016/j.jsv.2015.09.024
42. Yu X., Cheng L., You X. (2015), Hybrid silencers with micro-perforated panels and internal partitions, The Journal of the Acoustical Society of America, 137(2): 951–962, https://doi.org/10.1121/1.4906148
2. Allam S., Åbom M. (2011), A new type of muffler based on microperforated tubes, Journal of Vibration and Acoustics, 133(3): 031005, https://doi.org/10.1115/1.4002956
3. Beranek L.L. (1947), Acoustical properties of homogeneous, isotropic rigid tiles and flexible blankets, The Journal of the Acoustical Society of America, 19(4): 556–568, https://doi.org/10.1121/1.1916521
4. Bravo T., Elliott S.J. (2004), Variability of low frequency sound transmission measurements, The Journal of the Acoustical Society of America, 115(6): 2986–2997, https://doi.org/10.1121/1.1738452
5. Bravo T., Maury C., Pinhède C. (2012), Sound absorption and transmission through flexible microperforated panels backed by an air layer and a thin plate, The Journal of the Acoustical Society of America, 131(5): 3853–3863, https://doi.org/10.1121/1.3701987
6. Bravo T., Maury C., Pinhède C. (2014), Optimising the absorption and transmission properties of aircraft microperforated panels, Applied Acoustics, 79: 47–57, https://doi.org/10.1016/j.apacoust.2013.12.009
7. Bravo T., Maury C., Pinhède C. (2016), Optimisation of micro-perforated cylindrical silencers in linear and nonlinear regimes, Journal of Sound and Vibration, 363: 359–379, https://doi.org/10.1016/j.jsv.2015.11.011
8. Carneal J.P., Fuller C.R. (2004), An analytical and experimental investigation of active structural acoustic control of noise transmission through double panel system, Journal of Sound and Vibration, 272(3–5): 749–771, https://doi.org/10.1016/S0022-460X%2803%2900418-8
9. Chazot J.-D., Guyader J.-L. (2007), Prediction of transmission loss of double panels with a patch-mobility method, The Journal of the Acoustical Society of America, 121(1): 267–78, https://doi.org/10.1121/1.2395920
10. Cheng L., Li Y.Y., Gao J.X. (2005), Energy transmission in a mechanically-linked double-wall structure coupled to an acoustic enclosure, The Journal of the Acoustical Society of America, 117(5): 2742–2751, https://doi.org/10.1121/1.1886525
11. Chien W.Z. (1983), Method of high-order Lagrange multiplier and generalized variational principles of elasticity with more general forms of functional, Applied Mathematics and Mechanics, 4: 143–157, https://doi.org/10.1007/BF01895439
12. Delany M.E., Bazley E.N. (1970), Acoustical properties of fibrous materials, Applied Acoustics, 3(2): 105–116, https://doi.org/10.1016/0003-682X%2870%2990031-9
13. Du J.T., Li W.L., Liu Z.G., Xu H.A., Ji Z.L. (2011), Acoustic analysis of a rectangular cavity with general impedance boundary condition, The Journal of the Acoustical Society of America, 130(9): 807–817, https://doi.org/10.1121/1.3605534
14. Dupont T., Pavic G., Laulagnet B. (2003), Acoustic properties of lightweight micro-perforated plate systems, Acta Acustica united Acustica, 89(2): 201–212.
15. Falsafi I., Ohadi A. (2018), Optimisation of multistep cavity configuration to extend absorption bandwidth of micro perforated panel absorber, Archives of Acoustics, 43(2): 187–195, https://doi.org/10.24425/122366
16. Fuchs H.V., Zha X. (1997), Acrylic-glass sound absorbers in the plenum of the deutscher bundestag, Applied Acoustics, 51(2): 211–217, https://doi.org/10.1016/S0003-682X%2896%2900064-3
17. Gagliardini L., Roland J., Guyader J.L. (1991), The use of a functional basis to calculate acoustic transmission between rooms, Journal of Sound and Vibration, 145(3): 457–478, https://doi.org/10.1016/0022-460X (91)90114-Y.
18. Kang J., Brocklesby M.W. (2005), Feasibility of applying micro-perforated absorbers in acoustic window systems, Applied Acoustics, 66(6): 669–689, https://doi.org/10.1016/j.apacoust.2004.06.011
19. Kihlman T. (1967), Sound radiation into a rectangular room. Applications to airborne sound transmission in buildings, Acta Acustica, 18(1): 11–20.
20. Kim H.-S., Kim S.-R., Kim B.-K., Ma P.-S., Seo Y.-H. (2020a), Sound transmission loss of multilayered infinite micro-perforated plates, The Journal of the Acoustical Society of America, 147(1): 508–515, https://doi.org/10.1121/10.0000600
21. Kim H.-S., Ma P.-S., Kim B.-K., Lee S.-H., Seo Y.-H. (2020b), Sound transmission loss of multi-layered elastic micro-perforated plates in an impedance tube, Applied Acoustics, 166: 107348, https://doi.org/10.1016/j.apacoust.2020.107348
22. Kropp W., Pietrzyk A., Kihlman T. (1994), On the meaning of the sound reduction index at low frequencies, Acta Acustica (Les Ulis), 2(5): 379–392.
23. Liu Z., Zhan J., Fard M., Davy J.L. (2017), Acoustic properties of multilayer sound absorbers with a 3D printed micro-perforated panel, Applied Acoustics, 121: 25–32, https://doi.org/10.1016/j.apacoust.2017.01.032
24. Løvholt F., Norèn-Cosgriff K., Madshus C., Ellingsen S.E. (2017), Simulating low frequency sound transmission through walls and windows by a two-way coupled fluid structure interaction model, Journal of Sound and Vibration, 396: 203–216, https://doi.org/10.1016/j.jsv.2017.02.026
25. Maa D.-Y. (1998), Potential of microperforated panel absorber, The Journal of the Acoustical Society of America, 104(5): 2861–2866, https://doi.org/10.1121/1.423870
26. Meng H., Galland M.A., Ichchou M., Bareille O., Xin F.X., Lu T.J. (2017), Small perforations in corrugated sandwich panel significantly enhance low-frequency sound absorption and transmission loss, Composite Structures, 182: 1–11, https://doi.org/10.1016/j.compstruct.2017.08.103
27. Meng H., Galland M.A., Ichchou M., Xin F.X., Lu T.J. (2019), On the low-frequency acoustic properties of novel multifunctional honeycomb sandwich panels with micro-perforated faceplates, Applied Acoustics, 152: 31–40, https://doi.org/10.1016/j.apacoust.2019.02.028
28. Mu R.L., Toyoda M., Takahashi D. (2011a), Improvement of sound insulation performance of multilayer windows by using microperforated panel, Acoustical Science and Technology, 32(2): 79–81, https://doi.org/10.1250/ast.32.79
29. Mu R. L., Toyoda M., Takahashi D. (2011b), Sound insulation characteristics of multi-layer structures with a microperforated panel, Applied Acoustics, 72(11): 849–855, https://doi.org/10.1016/j.apacoust.2011.05.009
30. Mulholland K.A., Lyon R.H. (1973), Sound insulation at low frequencies, The Journal of the Acoustical Society of America, 54(4): 867–878, https://doi.org/10.1121/1.1914340
31. Osipov A., Mees P., Vermeir G. (1997a), Numerical simulations of airborne sound transmission at low frequencies: The influence of the room and the partition parameters, [in:] Proceedings of InterNoise 97, pp. 759–762.
32. Osipov A., Mees P., Vermeir G. (1997b), Low-frequency airborne sound transmission through single partitions in buildings, Applied Acoustics, 52(3–4): 273–288, https://doi.org/10.1016/S0003-682X%2897%2900031-5
33. Pfretzschner J., Cobo P., Simón F., Cuesta M., Fernández A. (2006), Microperforated insertion units: An alternative strategy to design microperforated panels, Applied Acoustics, 67(1): 62–73, https://doi.org/10.1016/j.apacoust.2005.05.005
34. Qu Y.G., Hua H.X., Meng G. (2013a), A domain decomposition approach for vibration analysis of isotropic and composite cylindrical shells with arbitrary boundaries, Composite Structures, 95: 307–321, https://doi.org/10.1016/j.compstruct.2012.06.022
35. Qu Y.G., Chen Y., Long X.H., Hua H.X., Meng G. (2013b), A modified variational approach for vibration analysis of ring-stiffened conical–cylindrical shell combinations, European Journal of Mechanics – A/Solids, 37: 200–215, https://doi.org/10.1016/j.euromechsol.2012.06.006
36. Takahashi D., Tanaka M. (2002), Flexural vibration of perforated plates and porous elastic materials under acoustic loading, Journal of the Acoustical Society of America, 112(4): 1456-1464, https://doi.org/10.1121/1.1497624
37. Tang Y., Xin F., Huang L., Lu T.J. (2017), Deep subwavelength acoustic metamaterial for low-frequency sound absorption, Europhysics Letters, 118(4): 44002, https://doi.org/10.1209/0295-5075/118/44002
38. Tang Y., Xin F., Huang L., Lu T.J. (2019), Sound absorption of micro-perforated sandwich panel with honeycomb-corrugation hybrid core at high temperatures, Composite Structures, 226: 111285, https://doi.org/10.1016/j.compstruct.2019.111285
39. Toyoda M., Takahashi D. (2008), Sound transmission through a microperforated-panel structure with subdivided air cavities, The Journal of the Acoustical Society of America, 124(6): 3594–3603, https://doi.org/10.1121/1.3001711
40. Xin F.X., Lu T.J., Chen C.Q. (2008), Vibroacoustic behavior of clamp mounted double-panel partition with enclosure air cavity, The Journal of the Acoustical Society of America, 124(6): 3604–3612, https://doi.org/10.1121/1.3006956
41. Yang C., Cheng L. (2016), Sound absorption of microperforated panels inside compact acoustic enclosures, Journal of Sound and Vibration, 360: 140–155, https://doi.org/10.1016/j.jsv.2015.09.024
42. Yu X., Cheng L., You X. (2015), Hybrid silencers with micro-perforated panels and internal partitions, The Journal of the Acoustical Society of America, 137(2): 951–962, https://doi.org/10.1121/1.4906148
