A Honeycomb Based Graded Metamaterial Muffler with Broadband Sound Attenuation and Load Bearing Performances
Abstract
A challenge for developing acoustic metamaterials (AMMs) is considering the application of broadband muffling and load bearing capacity simultaneously. In this paper, a honeycomb based graded AMM muffler is proposed, which can widen the attenuation band and improve the structural stiffness without any external device by means of integrated design. Firstly, the acoustic and mechanical characteristics of the muffler unit cell are theoretically and numerically studied, and the graded muffler is designed based on these characteristics. The numerical results show that the graded muffler widens the attenuation bandwidth of the unit cell, and the simulation also shows that the graded muffler has greater stiffness than the uniform one. The stiffness driven muffler provides new possibilities for the design of advanced metamaterial with simultaneous sound insulation and load bearing performances.Keywords:
acoustic metamaterials, honeycomb structure, phononic crystal, local resonance.References
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31. Naebe M., Shirvanimoghaddam K. (2016), Functionally graded materials: A review of fabrication and properties, Applied Materials Today, 5: 223–245, https://doi.org/10.1016/j.apmt.2016.10.001
32. Narayanamurti V., Strömer H.L., Chin M.A., Gossard A.C., Wiegmann W. (1979), Selective transmission of high-frequency phonons by a superlattice: the “dielectric” phonon filter, Physical Review Letters, 43(27): 2012–2016, https://doi.org/10.1103/PhysRevLett.43.2012
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37. Shen H.-S. (2002), Postbuckling analysis of axially loaded functionally graded cylindrical panels in thermal environments, International Journal of Solids and Structures, 39(24): 5991–6010, https://doi.org/10.1016/S0020-7683%2802%2900479-1
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42. Wang G., Chen S. (2015), Large low-frequency vibration attenuation induced by arrays of piezoelectric patches shunted with amplifier–resonator feedback circuits, Smart Materials and Structures, 25(1): 15004, https://doi.org/10.1088/0964-1726/25/1/015004
43. Wang G., Wang J., Chen S., Wen J. (2011), Vibration attenuations induced by periodic arrays of piezoelectric patches connected by enhanced resonant shunting circuits, Smart Materials and Structures, 20(12): 125019, https://doi.org/10.1088/0964-1726/20/12/125019
44. Wang T., An J., He H., Wen X., Xi X. (2021), A novel 3D impact energy absorption structure with negative Poisson’s ratio and its application in aircraft crashworthiness, Composite Structures, 262: 113663, https://doi.org/10.1016/j.compstruct.2021.113663
45. Wang Z. (2019), Recent advances in novel metallic honeycomb structure, Composites Part B: Engineering, 166: 731–741, https://doi.org/10.1016/j.compositesb.2019.02.011
46. Wang Z., Liu J. (2018), Mechanical performance of honeycomb filled with circular CFRP tubes, Composites Part B: Engineering, 135: 232–241, https://doi.org/10.1016/j.compositesb.2017.09.048
47. Wang Z., Liu J. (2019), Numerical and theoretical analysis of honeycomb structure filled with circular aluminum tubes subjected to axial compression, Composites Part B: Engineering, 165: 626–635, https://doi.org/10.1016/j.compositesb.2019.01.070
48. Xiang J., Du J. (2017), Energy absorption characteristics of bio-inspired honeycomb structure under axial impact loading, Materials Science and Engineering: A, 696: 283–289, https://doi.org/10.1016/j.msea.2017.04.044
49. Xiao S., Ma G., Li Y., Yang Z., Sheng P. (2015), Active control of membrane-type acoustic metamaterial by electric field, Applied Physics Letters, 106(9), https://doi.org/10.1063/1.4913999
50. Zarei Mahmoudabadi M., Sadighi M. (2011), A study on the static and dynamic loading of the foam filled metal hexagonal honeycomb – Theoretical and experimental, Materials Science and Engineering: A, 530: 333–343, https://doi.org/10.1016/j.msea.2011.09.093
51. Zhou J., Wang K., Xu D., Ouyang H. (2017), Multi-low-frequency flexural wave attenuation in Euler–Bernoulli beams using local resonators containing negative-stiffness mechanisms, Physics Letters A, 381(37): 3141–3148, https://doi.org/10.1016/j.physleta.2017.08.020
2. Asprone D., Auricchio F., Menna C., Morganti S., Prota A., Reali A. (2013), Statistical finite element analysis of the buckling behavior of honeycomb structures, Composite Structures, 105: 240–255, https://doi.org/10.1016/j.compstruct.2013.05.014
3. Bloch F. (1929), About the quantum mechanics of electrons in crystal lattices [in German], Zeitschrift für Physik, 52(7): 555–600, https://doi.org/10.1007/BF01339455
4. Brennan M.J. (1997), Characteristics of a wideband vibration neutralizer, Noise Control Engineering Journal, 45(5): 201–207, https://doi.org/10.3397/1.2828441
5. Camata G., Shing P.B. (2010), Static and fatigue load performance of a GFRP honeycomb bridge deck, Composites Part B: Engineering, 41(4): 299–307, https://doi.org/10.1016/j.compositesb.2010.02.005
6. Chen Q. et al. (2016), Plastic collapse of cylindrical shell-plate periodic honeycombs under uniaxial compression: experimental and numerical analyses, International Journal of Mechanical Sciences, 111–112: 125–133, https://doi.org/10.1016/j.ijmecsci.2016.03.020
7. Chen W.Q., Lee K.Y. (2003), Alternative state space formulations for magnetoelectric thermoelasticity with transverse isotropy and the application to bending analysis of nonhomogeneous plates, International Journal of Solids and Structures, 40(21): 5689–5705, https://doi.org/10.1016/S0020-7683%2803%2900339-1
8. Chen X., Xu X., Ai S., Chen H., Pei Y., Zhou X. (2014), Active acoustic metamaterials with tunable effective mass density by gradient magnetic fields, Applied Physics Letters, 105(7): 071913, https://doi.org/10.1063/1.4893921
9. Chen Y., Chen G., Li G., He H. (2021a), Modal analysis of flexural band gaps in a membrane acoustic metamaterial (MAM) and waveguides affected by shape characteristics, Physics Letters A, 414: 127635, https://doi.org/10.1016/j.physleta.2021.127635
10. Chen Y., Li G., Sun R., Chen G. (2021b), Wave dispersion in one-dimensional nonlinear local resonance phononic crystals with perturbation method, Crystals, 11(7): 1–15, https://doi.org/10.3390/cryst11070774
11. Cheng Z.-Q. (2001), Nonlinear bending of inhomogeneous plates, Engineering Structures, 23(10): 1359–1363, https://doi.org/10.1016/S0141-0296%2801%2900017-7
12. Correa D.M., Seepersad C.C., Haberman M.R. (2015), Mechanical design of negative stiffness honeycomb materials, Integrating Materials and Manufacturing Innovation, 4(1): 165–175, https://doi.org/10.1186/s40192-015-0038-8
13. Deymier P.A. [Ed.] (2013), Acoustic Metamaterials and Phononic Crystals, Springer, https://doi.org/10.1007/978-3-642-31232-8
14. Ding Y., Liu Z., Qiu C., Shi J. (2007), Metamaterial with simultaneously negative bulk modulus and mass density, Physical Review Letters, 99(9): 2–5, https://doi.org/10.1103/PhysRevLett.99.093904
15. Fan X., Verpoest I., Vandepitte D. (2006), Finite element analysis of out-of-plane compressive properties of thermoplastic honeycomb, Journal of Sandwich Structures & Materials, 8(5): 437–458, https://doi.org/10.1177/1099636206065862
16. Han B., Wang W., Zhang Z., Zhang Q., Jin F., Lu T. (2016), Performance enhancement of sandwich panels with honeycomb–corrugation hybrid core, Theoretical and Applied Mechanics Letters, 6(1): 54–59, https://doi.org/10.1016/j.taml.2016.01.001
17. Huang J., Gong X., Zhang Q., Scarpa F., Liu Y., Leng J. (2016), In-plane mechanics of a novel zero Poisson’s ratio honeycomb core, Composites Part B: Engineering, 89: 67–76, https://doi.org/10.1016/j.compositesb.2015.11.032
18. Jabbari M., Sohrabpour S. (2014), Mechanical and thermal stresses in a functionally graded hollow cylinder due to nonaxisymmetric steady-state loads, [in:] Encyclopedia of Thermal Stresses, Hetnarski R.B. [Ed.], pp. 2946–2952, Springer, Dordrecht, https://doi.org/10.1007/978-94-007-2739-7_959
19. Junger M.C., Feit D. (1986), Sound, structures, and their interaction, The MIT Press: Cambridge, Massachusetts, London, England.
20. Kawasaki A., Watanabe R. (1997), Concept and P/M fabrication of functionally gradient materials, Ceramics International, 23(1): 73–83, https://doi.org/10.1016/0272-8842%2895%2900143-3
21. Khan M.K., Baig T., Mirza S. (2012), Experimental investigation of in-plane and out-of-plane crushing of aluminum honeycomb, Materials Science and Engineering: A, 539: 135–142, https://doi.org/10.1016/j.msea.2012.01.070
22. Koizumi M. (1997), FGM activities in Japan, Composites Part B: Engineering, 28(1–2): 1–4, https://doi.org/10.1016/S1359-8368%2896%2900016-9
23. Kushwaha M.S., Halevi P., Dobrzynski L., Djafari-Rouhani B. (1993), Acoustic band structure of periodic elastic composites, Physical Review Letters, 71(13): 2022–2025, https://doi.org/10.1103/PhysRevB.49.2313
24. Li Z., Wang T., Jiang Y., Wang L., Liu D. (2018), Design-oriented crushing analysis of hexagonal honeycomb core under in-plane compression, Composite Structures, 187: 429–438, https://doi.org/10.1016/j.compstruct.2017.12.066
25. Liu J., Wang Z., Hui D. (2018), Blast resistance and parametric study of sandwich structure consisting of honeycomb core filled with circular metallic tubes, Composites Part B: Engineering, 145: 261–269, https://doi.org/10.1016/j.compositesb.2018.03.005
26. Liu Z. et al. (2000), Locally resonant sonic materials, Science, 289(5485): 1734–1736, https://doi.org/10.1126/science.289.5485.1734
27. Liu Z., Chan C.T., Sheng P. (2005), Analytic model of phononic crystals with local resonances, Physical Review B – Condensed Matter and Materials Physics, 71(1): 1–8, https://doi.org/10.1103/PhysRevB.71.014103
28. Martínez-Sala R., Sancho J., Sánchez J.V., Gómez V., Llinares J., Meseguer F. (1995), Sound attenuation by sculpture, Nature, 378(6554): 241, https://doi.org/10.1038/378241a0
29. Michailidis P.A., Triantafyllidis N., Shaw J.A., Grummon D.S. (2009), Superelasticity and stability of a shape memory alloy hexagonal honeycomb under in-plane compression, International Journal of Solids and Structures, 46(13): 2724–2738, https://doi.org/10.1016/j.ijsolstr.2009.03.013
30. Montero de Espinosa F.R., Jiménez E., Torres M. (1998), Ultrasonic Band Gap in a Periodic Two-Dimensional Composite, Physical Review Letters, 80(6–9): 1208–1211, https://doi.org/10.1103/PhysRevLett.80.1208
31. Naebe M., Shirvanimoghaddam K. (2016), Functionally graded materials: A review of fabrication and properties, Applied Materials Today, 5: 223–245, https://doi.org/10.1016/j.apmt.2016.10.001
32. Narayanamurti V., Strömer H.L., Chin M.A., Gossard A.C., Wiegmann W. (1979), Selective transmission of high-frequency phonons by a superlattice: the “dielectric” phonon filter, Physical Review Letters, 43(27): 2012–2016, https://doi.org/10.1103/PhysRevLett.43.2012
33. Nishida E., Koopmann G.H. (2007), A method for designing and fabricating broadband vibration absorbers for structural noise control, Journal of Vibration and Acoustics, Transactions of the ASME, 129(4): 397–405, https://doi.org/10.1115/1.2424968
34. Popa B.I., Zigoneanu L., Cummer S.A. (2013), Tunable active acoustic metamaterials, Physical Review B – Condensed Matter and Materials Physics, 88(2): 1–8, https://doi.org/10.1103/PhysRevB.88.024303
35. Qian D., Shi Z. (2017), Using PWE/FE method to calculate the band structures of the semi-infinite PCs: periodic in x-y plane and finite in z−direction, Archives of Acoustics, 42(4): 735–742, https://doi.org/10.1515/aoa-2017-0076
36. Shao H., He H., Chen G., Chen Y. (2020), Two new designs of lamp-type piezoelectric metamaterials for active wave propagation control, Chinese Journal of Physics, 65: 1–13, https://doi.org/10.1016/j.cjph.2020.02.015
37. Shen H.-S. (2002), Postbuckling analysis of axially loaded functionally graded cylindrical panels in thermal environments, International Journal of Solids and Structures, 39(24): 5991–6010, https://doi.org/10.1016/S0020-7683%2802%2900479-1
38. Sigalas M.M., Economou E.N. (1992), Elastic and acoustic wave band structure, Journal of Sound and Vibration, 158(2): 377–382, https://doi.org/10.1016/0022-460X%2892%2990059-7
39. Sun G., Hou X., Chen D., Li Q. (2017), Experimental and numerical study on honeycomb sandwich panels under bending and in-panel compression, Materials & Design, 133: 154–168, https://doi.org/10.1016/j.matdes.2017.07.057
40. Tsukamoto H. (2003), Analytical method of inelastic thermal stresses in a functionally graded material plate by a combination of micro- and macromechanical approaches, Composites Part B: Engineering, 34(6): 561–568, https://doi.org/10.1016/S1359-8368%2802%2900037-9
41. Vasseur J.O., Deymier P.A., Frantziskonis G., Hong G., Djafari-Rouhani B., Dobrzynski L. (1998), Experimental evidence for the existence of absolute acoustic band gaps in two-dimensional periodic composite media, Journal of Physics: Condensed Matter, 10(27): 6051–6064, https://doi.org/10.1088/0953-8984/10/27/006
42. Wang G., Chen S. (2015), Large low-frequency vibration attenuation induced by arrays of piezoelectric patches shunted with amplifier–resonator feedback circuits, Smart Materials and Structures, 25(1): 15004, https://doi.org/10.1088/0964-1726/25/1/015004
43. Wang G., Wang J., Chen S., Wen J. (2011), Vibration attenuations induced by periodic arrays of piezoelectric patches connected by enhanced resonant shunting circuits, Smart Materials and Structures, 20(12): 125019, https://doi.org/10.1088/0964-1726/20/12/125019
44. Wang T., An J., He H., Wen X., Xi X. (2021), A novel 3D impact energy absorption structure with negative Poisson’s ratio and its application in aircraft crashworthiness, Composite Structures, 262: 113663, https://doi.org/10.1016/j.compstruct.2021.113663
45. Wang Z. (2019), Recent advances in novel metallic honeycomb structure, Composites Part B: Engineering, 166: 731–741, https://doi.org/10.1016/j.compositesb.2019.02.011
46. Wang Z., Liu J. (2018), Mechanical performance of honeycomb filled with circular CFRP tubes, Composites Part B: Engineering, 135: 232–241, https://doi.org/10.1016/j.compositesb.2017.09.048
47. Wang Z., Liu J. (2019), Numerical and theoretical analysis of honeycomb structure filled with circular aluminum tubes subjected to axial compression, Composites Part B: Engineering, 165: 626–635, https://doi.org/10.1016/j.compositesb.2019.01.070
48. Xiang J., Du J. (2017), Energy absorption characteristics of bio-inspired honeycomb structure under axial impact loading, Materials Science and Engineering: A, 696: 283–289, https://doi.org/10.1016/j.msea.2017.04.044
49. Xiao S., Ma G., Li Y., Yang Z., Sheng P. (2015), Active control of membrane-type acoustic metamaterial by electric field, Applied Physics Letters, 106(9), https://doi.org/10.1063/1.4913999
50. Zarei Mahmoudabadi M., Sadighi M. (2011), A study on the static and dynamic loading of the foam filled metal hexagonal honeycomb – Theoretical and experimental, Materials Science and Engineering: A, 530: 333–343, https://doi.org/10.1016/j.msea.2011.09.093
51. Zhou J., Wang K., Xu D., Ouyang H. (2017), Multi-low-frequency flexural wave attenuation in Euler–Bernoulli beams using local resonators containing negative-stiffness mechanisms, Physics Letters A, 381(37): 3141–3148, https://doi.org/10.1016/j.physleta.2017.08.020
