Improving Sound Insulation in Low Frequencies by a Three-Component Cladding Acoustic Metamaterial Panel
Abstract
In this paper, a three-component cladding acoustic metamaterial panel with good sound insulation effect in the low-frequency range is proposed. The sound transmission loss of metamaterial panels under different structural configurations and different material parameters is investigated by combining finite element simulation calculations with experimental research. The results show that the closer the center of gravity of the scatterer is to the substrate, the better the stability of the resonance unit, the wider the range of effective sound isolation frequencies, and the higher the degree of normalization. The filling rate of the scatterer is maintained at about 0.5 to obtain a better sound insulation effect. At the same time, choosing lower density materials for the substrate and metal materials with high density and high modulus of elasticity for the scatterer can maximally widen the bandgap and allows for low-frequency sound insulation below 600 Hz. This approach improves the low-frequency sound insulation efficiency of acoustic metamaterials. The results provide important explanations and references for a deeper understanding of the sound insulation mechanism and the effects of different parameters on sound insulation.Keywords:
acoustics, acoustic metamaterial panels, sound insulation properties, local resonance, low frequency sound insulationReferences
1. Atmojo A.Y. et al. (2021), ANC Gen1: BBTA3-BPPT 1st prototype of active noise control for vehicle cabin noise, [in:] Journal of Physics: Conference Series, 1951(1): 012030, https://doi.org/10.1088/1742-6596/1951/1/012030
2. Badreddine Assouar M., Oudich M. (2012), Enlargement of a locally resonant sonic band gap by using double-sides stubbed phononic plates, Applied Physics Letters, 100(12): 123506, https://doi.org/10.1063/1.3696050
3. Badreddine Assouar M., Senesi M., Oudich M., Ruzzene M., Hou Z. (2012), Broadband plate-type acoustic metamaterial for low-frequency sound attenuation, Applied Physics Letters, 101(17): 173505, https://doi.org/10.1063/1.4764072
4. Chen D., Zi H., Li Y., Li X. (2021), Low frequency ship vibration isolation using the band gap concept of sandwich plate-type elastic metastructures, Ocean Engineering, 235: 109460, https://doi.org/10.1016/j.oceaneng.2021.109460
5. He X.D., Wen J.H. (2018), Study on the effect of lattice constants on the sound insulation properties of acoustic metamaterial plates, Noise and Vibration Control (S1), pp. 51–55.
6. Hsu J.C. (2011), Local resonances-induced low-frequency band gaps in two-dimensional phononic crystal slabs with periodic stepped resonators, Journal of Physics D: Applied Physics, 44(5): 055401, doi: 10.1088/ 0022-3727/44/5/055401.
7. Hsu J.C., Wu T.T., Hsu H.S. (2013), Measurement of frequency gaps and waveguiding in phononic plates with periodic stepped cylinders using pulsed laser generated ultrasound, Journal of Applied Physics, 113(8): 083511, https://doi.org/10.1063/1.4793491
8. Iannac G., Ciaburro G., Trematerra A. (2021), Metamaterials acoustic barrier, Applied Acoustics, 181: 108172, https://doi.org/10.1016/j.apacoust.2021.108172
9. Jiang C., Moreau D., Fischer J., Doolan C. (2021), Additively manufactured sound-absorbing porous structures for airfoil trailing-edge noise control, Journal of Aerospace Engineering, 34(5): 04021068, https://doi.org/10.1061/%28ASCE%29AS.1943-5525.0001317
10. Li S., Chen T.,Wang X., Li Y., Chen W. (2016), Expansion of lower-frequency locally resonant band gaps using a double-sided stubbed composite phononic crystals plate with composite stubs, Physics Letters A, 380(25–26): 2167–2172, https://doi.org/10.1016/j.physleta.2016.03.027
11. Li Y., Chen T., Wang X., Xi Y., Liang Q. (2015), Enlargement of locally resonant sonic band gap by using composite plate-type acoustic metamaterial, Physics Letters A, 379(5): 412–416, https://doi.org/10.1016/j.physleta.2014.11.028
12. Liang B., Yuan B., Cheng J.C. (2009), Acoustic diode: Rectification of acoustic energy flux in one-dimensional systems, Physical Review Letters, 103(10): 104301, https://doi.org/10.1103/PhysRevLett.103.104301
13. Ma C., Shao C., Wan Q., Wang X., Cheng Y., Liu X. (2018), A locally-resonant phononic crystal for low-frequency vibration control of vehicle [in Chinese], Journal of Applied Acoustics, 37(1): 152–158, https://doi.org/10.11684/j.issn.1000-310X.2018.01.022
14. Maldovan M. (2013), Sound and heat revolutions in phononics, Nature, 503(7475): 209–217, https://doi.org/10.1038/nature12608
15. Nakayama M. et al. (2021), A practically designed acoustic metamaterial sheet with two-dimensional connection of local resonators for sound insulation applications, Journal of Applied Physics, 129(10): 105106, https://doi.org/10.1063/5.0041738
16. Oudich M. et al. (2011), Experimental evidence of locally resonant sonic band gap in two-dimensional phononic stubbed plates, Physical Review B, 84(16): 165136, https://doi.org/10.1103/PhysRevB.84.165136
17. Oudich M., Li Y., Assouar B.M., Hou Z. (2010), A sonic band gap based on the locally resonant phononic plates with stubs, New Journal of Physics, 12(8): 083049, https://doi.org/10.1088/1367-2630/12/8/083049
18. Pennec Y., Djafari-Rouhani B., Larabi H., Vasseur J.O., Hladky-Hennion A.C. (2008), Low-frequency gaps in a phononic crystal constituted of cylindrical dots deposited on a thin homogeneous plate, Physical Review B, 78(10): 104105, https://doi.org/10.1103/PhysRevB.78.104105
19. Qiu C., Liu Z. (2006), Acoustic directional radiation and enhancement caused by band-edge states of two-dimensional phononic crystals, Applied Physics Letters, 89(6): 063106, https://doi.org/10.1063/1.2335975
20. Song Y.B., Wen J., Yu D., Wen X. (2015), Suppression of vibration and noise radiation in a flexible floating raft system using periodic structures, Journal of Vibration and Control, 21(2), 217–228, https://doi.org/10.1177/1077 546313488156.
21. Wen J., Wang G., Yu D., Zhao H., Liu Y. (2005), Theoretical and experimental investigation of flexural wave propagation in straight beams with periodic structures: Application to a vibration isolation structure, Journal of Applied Physics, 97(11): 114907, https://doi.org/10.1063/1.1922068
22. Wen J.H., Wang G., Yu D.L., Zhao H.G., Liu Y.Z. Wen X.S. (2008), Study on the vibration band gap and vibration attenuation property of phononic crystals, Science in China Series E: Technological Sciences, 51: 85–99,https://doi.org/10.1007/s11431-008-0008-x
23. Yang Q. et al. (2020), Simulations on the wide bandgap characteristics of a two-dimensional tapered scatterer phononic crystal slab at low frequency, Physics Letters A, 384(35): 126885, https://doi.org/10.1016/j.physleta.2020.126885
24. Yin J. et al. (2022), Review on research progress of mechanical metamaterials and their applications on vibration and noise control [in Chinese], Advance in Mechanics, 52(3): 508–586, https://doi.org/10.6052/1000-0992-22-005
25. Yu K., Chen T., Wang X. (2013), Band gaps in the low-frequency range based on the two-dimensional phononic crystal plates composed of rubber matrix with periodic steel stubs, Physica B: Condensed Matter, 416: 12–16, https://doi.org/10.1016/j.physb.2013.02.011
26. Zhang J., Yao H., Du J., Zhao J., Dong Y., Qi P. (2016a), Low frequency sound insulation characteristics of the locally resonant phononic crystals in the large aircraft cabin [in Chinese], Journal of the Chinese Ceramic Society, 44(10): 1440–1445, https://doi.org/10.14062/j.issn.0454-5648.2016.10.08
27. Zhang H., Xiao Y., Wen J., Yu D., Wen X. (2016b), Ultra-thin smart acoustic metasurface for low-frequency sound insulation, Applied Physics Letters, 108(14): 141902, https://doi.org/10.1063/1.4945664
28. Zhao H. J., Guo H.W., Gao M.X., Liu R.Q., Deng Z.Q. (2016), Vibration band gaps in double-vibrator pillared phononic crystal plate, Journal of Applied Physics, 119(1): 014903, https://doi.org/10.1063/1.4939484
29. Zhao H.J., Guo H.W., Li B.Y., Deng Z.Q., Liu R.Q. (2015), Flexural vibration band gaps in a double-side phononic crystal plate, Journal of Applied Physics, 118(4): 044906, https://doi.org/10.1063/1.4927627
30. Zhou P., Wan S., Wang X., Fu J., Zhu Y. (2021), A novel hybrid composite phononic crystal plate with multiple vibration band gaps at low frequencies, Physica B: Condensed Matter, 623: 413366, https://doi.org/10.1016/j.physb.2021.413366
31. Zhou X., Wang L., Qin L., Peng F. (2020), Improving sound insulation in low frequencies by multiple band-gaps in plate-type acoustic metamaterials, Journal of Physics and Chemistry of Solids, 146: 109606, https://doi.org/10.1016/j.jpcs.2020.109606
32. Zuo K.C. (2016), Current status of research on aircraft cabin noise, Journal of Aviation, 37(8): 2370–2384.
2. Badreddine Assouar M., Oudich M. (2012), Enlargement of a locally resonant sonic band gap by using double-sides stubbed phononic plates, Applied Physics Letters, 100(12): 123506, https://doi.org/10.1063/1.3696050
3. Badreddine Assouar M., Senesi M., Oudich M., Ruzzene M., Hou Z. (2012), Broadband plate-type acoustic metamaterial for low-frequency sound attenuation, Applied Physics Letters, 101(17): 173505, https://doi.org/10.1063/1.4764072
4. Chen D., Zi H., Li Y., Li X. (2021), Low frequency ship vibration isolation using the band gap concept of sandwich plate-type elastic metastructures, Ocean Engineering, 235: 109460, https://doi.org/10.1016/j.oceaneng.2021.109460
5. He X.D., Wen J.H. (2018), Study on the effect of lattice constants on the sound insulation properties of acoustic metamaterial plates, Noise and Vibration Control (S1), pp. 51–55.
6. Hsu J.C. (2011), Local resonances-induced low-frequency band gaps in two-dimensional phononic crystal slabs with periodic stepped resonators, Journal of Physics D: Applied Physics, 44(5): 055401, doi: 10.1088/ 0022-3727/44/5/055401.
7. Hsu J.C., Wu T.T., Hsu H.S. (2013), Measurement of frequency gaps and waveguiding in phononic plates with periodic stepped cylinders using pulsed laser generated ultrasound, Journal of Applied Physics, 113(8): 083511, https://doi.org/10.1063/1.4793491
8. Iannac G., Ciaburro G., Trematerra A. (2021), Metamaterials acoustic barrier, Applied Acoustics, 181: 108172, https://doi.org/10.1016/j.apacoust.2021.108172
9. Jiang C., Moreau D., Fischer J., Doolan C. (2021), Additively manufactured sound-absorbing porous structures for airfoil trailing-edge noise control, Journal of Aerospace Engineering, 34(5): 04021068, https://doi.org/10.1061/%28ASCE%29AS.1943-5525.0001317
10. Li S., Chen T.,Wang X., Li Y., Chen W. (2016), Expansion of lower-frequency locally resonant band gaps using a double-sided stubbed composite phononic crystals plate with composite stubs, Physics Letters A, 380(25–26): 2167–2172, https://doi.org/10.1016/j.physleta.2016.03.027
11. Li Y., Chen T., Wang X., Xi Y., Liang Q. (2015), Enlargement of locally resonant sonic band gap by using composite plate-type acoustic metamaterial, Physics Letters A, 379(5): 412–416, https://doi.org/10.1016/j.physleta.2014.11.028
12. Liang B., Yuan B., Cheng J.C. (2009), Acoustic diode: Rectification of acoustic energy flux in one-dimensional systems, Physical Review Letters, 103(10): 104301, https://doi.org/10.1103/PhysRevLett.103.104301
13. Ma C., Shao C., Wan Q., Wang X., Cheng Y., Liu X. (2018), A locally-resonant phononic crystal for low-frequency vibration control of vehicle [in Chinese], Journal of Applied Acoustics, 37(1): 152–158, https://doi.org/10.11684/j.issn.1000-310X.2018.01.022
14. Maldovan M. (2013), Sound and heat revolutions in phononics, Nature, 503(7475): 209–217, https://doi.org/10.1038/nature12608
15. Nakayama M. et al. (2021), A practically designed acoustic metamaterial sheet with two-dimensional connection of local resonators for sound insulation applications, Journal of Applied Physics, 129(10): 105106, https://doi.org/10.1063/5.0041738
16. Oudich M. et al. (2011), Experimental evidence of locally resonant sonic band gap in two-dimensional phononic stubbed plates, Physical Review B, 84(16): 165136, https://doi.org/10.1103/PhysRevB.84.165136
17. Oudich M., Li Y., Assouar B.M., Hou Z. (2010), A sonic band gap based on the locally resonant phononic plates with stubs, New Journal of Physics, 12(8): 083049, https://doi.org/10.1088/1367-2630/12/8/083049
18. Pennec Y., Djafari-Rouhani B., Larabi H., Vasseur J.O., Hladky-Hennion A.C. (2008), Low-frequency gaps in a phononic crystal constituted of cylindrical dots deposited on a thin homogeneous plate, Physical Review B, 78(10): 104105, https://doi.org/10.1103/PhysRevB.78.104105
19. Qiu C., Liu Z. (2006), Acoustic directional radiation and enhancement caused by band-edge states of two-dimensional phononic crystals, Applied Physics Letters, 89(6): 063106, https://doi.org/10.1063/1.2335975
20. Song Y.B., Wen J., Yu D., Wen X. (2015), Suppression of vibration and noise radiation in a flexible floating raft system using periodic structures, Journal of Vibration and Control, 21(2), 217–228, https://doi.org/10.1177/1077 546313488156.
21. Wen J., Wang G., Yu D., Zhao H., Liu Y. (2005), Theoretical and experimental investigation of flexural wave propagation in straight beams with periodic structures: Application to a vibration isolation structure, Journal of Applied Physics, 97(11): 114907, https://doi.org/10.1063/1.1922068
22. Wen J.H., Wang G., Yu D.L., Zhao H.G., Liu Y.Z. Wen X.S. (2008), Study on the vibration band gap and vibration attenuation property of phononic crystals, Science in China Series E: Technological Sciences, 51: 85–99,https://doi.org/10.1007/s11431-008-0008-x
23. Yang Q. et al. (2020), Simulations on the wide bandgap characteristics of a two-dimensional tapered scatterer phononic crystal slab at low frequency, Physics Letters A, 384(35): 126885, https://doi.org/10.1016/j.physleta.2020.126885
24. Yin J. et al. (2022), Review on research progress of mechanical metamaterials and their applications on vibration and noise control [in Chinese], Advance in Mechanics, 52(3): 508–586, https://doi.org/10.6052/1000-0992-22-005
25. Yu K., Chen T., Wang X. (2013), Band gaps in the low-frequency range based on the two-dimensional phononic crystal plates composed of rubber matrix with periodic steel stubs, Physica B: Condensed Matter, 416: 12–16, https://doi.org/10.1016/j.physb.2013.02.011
26. Zhang J., Yao H., Du J., Zhao J., Dong Y., Qi P. (2016a), Low frequency sound insulation characteristics of the locally resonant phononic crystals in the large aircraft cabin [in Chinese], Journal of the Chinese Ceramic Society, 44(10): 1440–1445, https://doi.org/10.14062/j.issn.0454-5648.2016.10.08
27. Zhang H., Xiao Y., Wen J., Yu D., Wen X. (2016b), Ultra-thin smart acoustic metasurface for low-frequency sound insulation, Applied Physics Letters, 108(14): 141902, https://doi.org/10.1063/1.4945664
28. Zhao H. J., Guo H.W., Gao M.X., Liu R.Q., Deng Z.Q. (2016), Vibration band gaps in double-vibrator pillared phononic crystal plate, Journal of Applied Physics, 119(1): 014903, https://doi.org/10.1063/1.4939484
29. Zhao H.J., Guo H.W., Li B.Y., Deng Z.Q., Liu R.Q. (2015), Flexural vibration band gaps in a double-side phononic crystal plate, Journal of Applied Physics, 118(4): 044906, https://doi.org/10.1063/1.4927627
30. Zhou P., Wan S., Wang X., Fu J., Zhu Y. (2021), A novel hybrid composite phononic crystal plate with multiple vibration band gaps at low frequencies, Physica B: Condensed Matter, 623: 413366, https://doi.org/10.1016/j.physb.2021.413366
31. Zhou X., Wang L., Qin L., Peng F. (2020), Improving sound insulation in low frequencies by multiple band-gaps in plate-type acoustic metamaterials, Journal of Physics and Chemistry of Solids, 146: 109606, https://doi.org/10.1016/j.jpcs.2020.109606
32. Zuo K.C. (2016), Current status of research on aircraft cabin noise, Journal of Aviation, 37(8): 2370–2384.
