Abstract
This review article is concerned with metamaterials, i.e. specifically engineered structures with special properties for interaction with sounds. The research on and practical design of these materials have gained momentum in the last decade, when 3D printing techniques provided the possibility to fabricate such geometrically complex structures. We briefly describe the history of research on AMMs and group them into active and passive metamaterials. For each of these groups of AMMs, we discuss the most notable construction achievements and outline the main applications. We conclude this review with a discussion of possible directions for further research and main applications of AMMs such as noise attenuation, acoustic lens, and the cloaking phenomenon.Keywords:
acoustic metamaterials, acoustic metasufraces, tunability, 3D printing.References
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2. Akl W., Baz A. (2021), Active control of the dynamic density of acoustic metamaterials, Applied Acoustics, 178: 108001, https://doi.org/10.1016/j.apacoust.2021.108001
3. Allam A., Elsabbagh A., Akl W. (2017), Experimental demonstration of one-dimensional active platetype acoustic metamaterial with adaptive programmable density, Journal of Applied Physics, 121(12): 125106, https://doi.org/10.1063/1.4979020
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5. Carcione J.M., Cavallini F. (1995), On the acousticelectromagnetic analogy, Wave Motion, 21(2): 149–162, https://doi.org/10.1016/0165-2125%2894%2900047-9
6. Carcione J.M., Robinson E. (2002), On the acousticelectromagnetic analogy for the reflection-refraction problem, Studia Geophysica et Geodaetica, 46(2): 321–346, https://doi.org/10.1023/A%3A1019862321912
7. Chen Z. et al. (2016), A tunable acoustic metamaterial with double-negativity driven by electromagnets, Scientific Reports, 6(1): 30254, https://doi.org/10.1038/srep30254
8. Csernyava O. (2021), Anisotropic Cloak FDTD (version 1.3). MATLAB Central File Exchange, https://www.mathworks.com/matlabcentral/fileexchange/73120-anisotropic-cloak-fdtd
9. Cummer S.A., Christensen J., Alù A. (2016), Controlling sound with acoustic metamaterials, Nature Reviews Materials, 1(3): 16001, https://doi.org/10.1038/natrevmats.2016.1
10. Cummer S.A., Schurig D. (2007), One path to acoustic cloaking, New Journal of Physics, 9(3): 45–45, https://doi.org/10.1088/1367-2630/9/3/045
11. Dong H.W., Zhao S.D., Wei P., Cheng L., Wang Y.S., Zhang C. (2019), Systematic design and realization of double-negative acoustic metamaterials by topology optimization, Acta Materialia, 172: 102–120, https://doi.org/10.1016/j.actamat.2019.04.042
12. Enoch J.M. (1999), Remarkable lenses and eye units in statues from the Egyptian Old Kingdom (ca. 4500 years ago): properties, timeline, questions requiring resolution, [in:] 18th Congress of the International Commission for Optics: Vol. Proc. SPIE, A.J. Glass, J.W. Goodman, M. Chang, A.H. Guenther, T. Asakura [Eds], pp. 224–225, https://doi.org/10.1117/12.354722
13. Esfahlani H., Karkar S., Lissek H. (2016), Acoustic carpet cloak based on an ultrathin metasurface, Physical Review, 94(1): 014302, https://doi.org/10.1103/PhysRevB.94.014302
14. Fang N. et al. (2006), Ultrasonic metamaterials with negative modulus, Nature Materials, 5(6): 452–456, https://doi.org/10.1038/nmat1644
15. Fang N., Xu J., Nemati N., Viard N., Lafarge D. (2018), Acoustic metamaterial, [in:] World Scientific Handbook of Metamaterials and Plasmonics, Volume 2: Elastic, Acoustic, and Seismic Metamaterials, R. Craster, S. Guenneau [Eds],World Scientific Publishing Co. Pte. Ltd., 10.1142/10642-vol2.
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18. Langfeldt F., Riecken J., Gleine W., von Estorff O., (2016), A membrane-type acoustic metamaterial with adjustable acoustic properties, Journal of Sound and Vibration, 373: 1–18, https://doi.org/10.1016/j.jsv.2016.03.025
19. Lee K.J.B., Jung M.K., Lee S.H. (2012), Highly tunable acoustic metamaterials based on a resonant tubular array, Physical Review B, 86(18): 184302, https://doi.org/10.1103/PhysRevB.86.184302
20. Lee S.H., Park C.M., Seo Y.M., Wang Z.G., Kim C.K. (2009), Acoustic metamaterial with negative density, Physics Letters, Section A: General, Atomic and Solid State Physics, 373(48): 4464–4469, https://doi.org/10.1016/j.physleta.2009.10.013
21. Lee S.H., Park C.M., Seo Y.M., Wang Z.G., Kim C.K. (2010), Composite acoustic medium with simultaneously negative density and modulus, Physical Review Letters, 104(5): 1–4, https://doi.org/10.1103/PhysRevLett.104.054301
22. Leonhardt U. (2006), Optical conformal mapping, Science, 312(5781): 1777–1780, https://doi.org/10.1126/science.1126493
23. Li J., Chan C.T. (2004), Double-negative acoustic metamaterial, Physical Review E – Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 70(5): 055602, https://doi.org/10.1103/PhysRevE.70.055602
24. Li P., Chen X., Zhou X., Hu G., Xiang P. (2015), Acoustic cloak constructed with thin-plate metamaterials, International Journal of Smart and Nano Materials, 6(1): 73–83, https://doi.org/10.1080/19475411.2015.1005722
25. Lin Q., Lin Q., Wang Y., Di G. (2021), Sound insulation performance of sandwich structure compounded with a resonant acoustic metamaterial, Composite Structures, 273: 114312, https://doi.org/10.1016/j.compstruct.2021.114312
26. Liu Y. et al. (2020), Three-dimensional fractal structure with double negative and density-near-zero properties on a subwavelength scale, Materials and Design, 188: 108470, https://doi.org/10.1016/j.matdes.2020.108470
27. Liu Z. et al. (2000), Locally resonant sonic materials, Science, 289(5485): 1734–1736, https://doi.org/10.1126/science.289.5485.1734
28. Long H. et al. (2020), Subwavelength broadband sound absorber based on a composite metasurface, Scientific Reports, 10(1): 1–10, https://doi.org/10.1038/s41598-020-70714-7
29. Long M. (2014), Sound transmission loss, [in:] Architectural Acoustics, 2nd ed., pp. 345–382, Boston: Academic Press, https://doi.org/10.1016/b978-0-12-398258-2.00009-x
30. Mahesh N.R., Prita N. (2011), Experimental and theoretical investigation of acoustic metamaterial with negative bulk modulus, Proceedings of 2011 COMSOL Conference, https://www.comsol.com/paper/experimental-and-theoretical-investigation-of-acoustic-metamaterial-with-negativ-11440
31. Naify C.J., Ikei A., Rohde C.A. (2020), Locally programmable metamaterial elements using fourdimensional printing, Extreme Mechanics Letters, 36: 100654, https://doi.org/10.1016/j.eml.2020.100654
32. Nicolas L., Furstoss M., Galland M.A. (1998), Analogy electromagnetism-acoustics: Validation and application to local impedance active control for sound absorption, EPJ Applied Physics, 4(1): 95–100, https://doi.org/10.1051/epjap%3A1998247
33. Ning S., Yan Z., Chu D., Jiang H., Liu Z., Zhuang Z. (2021), Ultralow-frequency tunable acoustic metamaterials through tuning gauge pressure and gas temperature, Extreme Mechanics Letters, 44: 101218, https://doi.org/10.1016/j.eml.2021.101218
34. Pendry J.B. (2000), Negative refraction makes a perfect lens, Physical Review Letters, 85(18): 3966–3969, https://doi.org/10.1103/PhysRevLett.85.3966
35. Pendry J.B., Schurig D., Smith D.R. (2006), Controlling electromagnetic fields, Science, 312(1780): 1780–1782, https://doi.org/10.1126/science.1125907
36. Peng Y.G., Shen Y.X., Geng Z.G., Li P.Q., Zhu J., Zhu X.F. (2020), Super-resolution acoustic image montage via a biaxial metamaterial lens, Science Bulletin, 65(12): 1022–1029, https://doi.org/10.1016/j.scib.2020.03.018
37. 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
38. Sang Hoon K., Mukunda D. (2012), Seismic waveguide of metamaterials, Modern Physics Letters B, 26(17): 1250105, https://doi.org/10.1142/S0217984912501059
39. Sarvazyan A.P., Urban M.W., Greenleaf J.F. (2013), Acoustic waves in medical imaging and diagnostics, Ultrasound in Medicine and Biology, 39(7): 1133–1146, https://doi.org/10.1016/j.ultrasmedbio.2013.02.006
40. Shao C., Long H., Cheng Y., Liu X. (2019), Low-frequency perfect sound absorption achieved by a modulus-near-zero metamaterial, Scientific Reports, 9(1): 1–8, https://doi.org/10.1038/s41598-019-49982-5
41. Shao H., He H., Chen Y., Tan X., Chen G. (2020), A tunable metamaterial muffler with a membrane structure based on Helmholtz cavities, Applied Acoustics, 157: 107022, https://doi.org/10.1016/j.apacoust.2019.107022
42. Sirota L., Sabsovich D., Lahini Y., Ilan R., Shokef Y. (2021), Real-time steering of curved sound beams in a feedback-based topological acoustic metamaterial, Mechanical Systems and Signal Processing, 153: 107479, https://doi.org/10.1016/j.ymssp.2020.107479
43. Smith D.R., Padilla W.J., Vier D.C., Nemat-Nasser S.C., Schultz S. (2000), Composite medium with simultaneously negative permeability and permittivity, Physical Review Letters, 84(18): 4184–4187, https://doi.org/10.1103/PhysRevLett.84.4184
44. Veselago V.G. (1968), The electrodynamic of substances with simultaneous negative values of ε and μ, Soviet Physics Uspekhi, 10(4): 509–514, https://doi.org/10.1070/pu1968v010n04abeh003699
45. Walser R.M. (2001), Electromagnetic metamaterials, [in:] Complex Mediums II: Beyond Linear Isotropic Dielectrics, A. Lakhtakia, W.S. Weiglhofer, I.J. Hodgkinson [Eds], Vol. 4467, SPIE, https://doi.org/10.1117/12.432921
46. Xiao S. et al. (2015), Active control of membrane-type acoustic metamaterial by electric field, Applied Physics Letters, 106(9): 091904, https://doi.org/10.1063/1.4913999
47. Yang M., Ma G., Yang Z., Sheng P. (2013), Coupled membranes with doubly negative mass density and bulk modulus, Physical Review Letters, 110(13): 134301, https://doi.org/10.1103/PhysRevLett.110.134301
48. Yang Z., Mei J., Yang M., Chan N.H., Sheng P. (2008), Membrane-type acoustic metamaterial with negative dynamic mass, Physical Review Letters, 101(20): 1–4, https://doi.org/10.1103/PhysRevLett.101.204301
49. Zangeneh-Nejad F., Fleury R. (2019), Active times for acoustic metamaterials, Reviews in Physics, 4:100031, https://doi.org/10.1016/j.revip.2019.100031
50. Zhang H., Xiao Y., Wen J., Yu D., Wen X. (2016), Ultra-thin smart acoustic metasurface for lowfrequency sound insulation, Applied Physics Letters, 108(14): 141902, https://doi.org/10.1063/1.4945664
51. Zhang S. (2010), Acoustic metamaterial design and applications, Ph.D. Dissertation, Graduate College of the University of Illinois, http://hdl.handle.net/2142/16524
52. Zhang X., Qu Z.,Wang H. (2020), Engineering acoustic metamaterials for sound absorption: from uniform to gradient structures, iScience, 23(5): 101110, https://doi.org/10.1016/j.isci.2020.101110
53. Zielinski T.G. et al. (2020), Reproducibility of soundabsorbing periodic porous materials using additive manufacturing technologies: round robin study, Additive Manufacturing, 36: 101564, https://doi.org/10.1016/j.addma.2020.101564
54. Zigoneanu L., Popa B., Cummer S.A. (2014), Three-dimensional broadband omnidirectional acoustic ground cloak, Nature Materials, 13(4): 352–355, https://doi.org/10.1038/NMAT3901
55. Ziolkowski R.W. (2014), Metamaterials: The early years in the USA, EPJ Applied Metamaterials, 1: 5, https://doi.org/10.1051/epjam/2014004
2. Akl W., Baz A. (2021), Active control of the dynamic density of acoustic metamaterials, Applied Acoustics, 178: 108001, https://doi.org/10.1016/j.apacoust.2021.108001
3. Allam A., Elsabbagh A., Akl W. (2017), Experimental demonstration of one-dimensional active platetype acoustic metamaterial with adaptive programmable density, Journal of Applied Physics, 121(12): 125106, https://doi.org/10.1063/1.4979020
4. Born M., Wolf E. (1980), Elements of the theory of diffraction, [in:] Principles of Optics (Sixth Edition), Pergamon, pp. 370–458, https://doi.org/10.1016/B978-0-08-026482-0.50015-3
5. Carcione J.M., Cavallini F. (1995), On the acousticelectromagnetic analogy, Wave Motion, 21(2): 149–162, https://doi.org/10.1016/0165-2125%2894%2900047-9
6. Carcione J.M., Robinson E. (2002), On the acousticelectromagnetic analogy for the reflection-refraction problem, Studia Geophysica et Geodaetica, 46(2): 321–346, https://doi.org/10.1023/A%3A1019862321912
7. Chen Z. et al. (2016), A tunable acoustic metamaterial with double-negativity driven by electromagnets, Scientific Reports, 6(1): 30254, https://doi.org/10.1038/srep30254
8. Csernyava O. (2021), Anisotropic Cloak FDTD (version 1.3). MATLAB Central File Exchange, https://www.mathworks.com/matlabcentral/fileexchange/73120-anisotropic-cloak-fdtd
9. Cummer S.A., Christensen J., Alù A. (2016), Controlling sound with acoustic metamaterials, Nature Reviews Materials, 1(3): 16001, https://doi.org/10.1038/natrevmats.2016.1
10. Cummer S.A., Schurig D. (2007), One path to acoustic cloaking, New Journal of Physics, 9(3): 45–45, https://doi.org/10.1088/1367-2630/9/3/045
11. Dong H.W., Zhao S.D., Wei P., Cheng L., Wang Y.S., Zhang C. (2019), Systematic design and realization of double-negative acoustic metamaterials by topology optimization, Acta Materialia, 172: 102–120, https://doi.org/10.1016/j.actamat.2019.04.042
12. Enoch J.M. (1999), Remarkable lenses and eye units in statues from the Egyptian Old Kingdom (ca. 4500 years ago): properties, timeline, questions requiring resolution, [in:] 18th Congress of the International Commission for Optics: Vol. Proc. SPIE, A.J. Glass, J.W. Goodman, M. Chang, A.H. Guenther, T. Asakura [Eds], pp. 224–225, https://doi.org/10.1117/12.354722
13. Esfahlani H., Karkar S., Lissek H. (2016), Acoustic carpet cloak based on an ultrathin metasurface, Physical Review, 94(1): 014302, https://doi.org/10.1103/PhysRevB.94.014302
14. Fang N. et al. (2006), Ultrasonic metamaterials with negative modulus, Nature Materials, 5(6): 452–456, https://doi.org/10.1038/nmat1644
15. Fang N., Xu J., Nemati N., Viard N., Lafarge D. (2018), Acoustic metamaterial, [in:] World Scientific Handbook of Metamaterials and Plasmonics, Volume 2: Elastic, Acoustic, and Seismic Metamaterials, R. Craster, S. Guenneau [Eds],World Scientific Publishing Co. Pte. Ltd., 10.1142/10642-vol2.
16. Goelzer B., Hansen C.H., Sehrndt G.A. (2020), Occupational exposure to noise: evaluation, prevention and control, [in:] Document published on behalf of the World Health Organisation, Vol. 15, Issues 1–2, https://www.who.int/occupational_health/publications/occupnoise/en/ retrieved October 8, 2020.
17. Gruber D.P., Tew J.M. (1998), History of the operating microscope: from magnifying glass to microneurosurgery, Neurosurgery, 42(4): 907, https://doi.org/10.1097/00006123-199804000-00118
18. Langfeldt F., Riecken J., Gleine W., von Estorff O., (2016), A membrane-type acoustic metamaterial with adjustable acoustic properties, Journal of Sound and Vibration, 373: 1–18, https://doi.org/10.1016/j.jsv.2016.03.025
19. Lee K.J.B., Jung M.K., Lee S.H. (2012), Highly tunable acoustic metamaterials based on a resonant tubular array, Physical Review B, 86(18): 184302, https://doi.org/10.1103/PhysRevB.86.184302
20. Lee S.H., Park C.M., Seo Y.M., Wang Z.G., Kim C.K. (2009), Acoustic metamaterial with negative density, Physics Letters, Section A: General, Atomic and Solid State Physics, 373(48): 4464–4469, https://doi.org/10.1016/j.physleta.2009.10.013
21. Lee S.H., Park C.M., Seo Y.M., Wang Z.G., Kim C.K. (2010), Composite acoustic medium with simultaneously negative density and modulus, Physical Review Letters, 104(5): 1–4, https://doi.org/10.1103/PhysRevLett.104.054301
22. Leonhardt U. (2006), Optical conformal mapping, Science, 312(5781): 1777–1780, https://doi.org/10.1126/science.1126493
23. Li J., Chan C.T. (2004), Double-negative acoustic metamaterial, Physical Review E – Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 70(5): 055602, https://doi.org/10.1103/PhysRevE.70.055602
24. Li P., Chen X., Zhou X., Hu G., Xiang P. (2015), Acoustic cloak constructed with thin-plate metamaterials, International Journal of Smart and Nano Materials, 6(1): 73–83, https://doi.org/10.1080/19475411.2015.1005722
25. Lin Q., Lin Q., Wang Y., Di G. (2021), Sound insulation performance of sandwich structure compounded with a resonant acoustic metamaterial, Composite Structures, 273: 114312, https://doi.org/10.1016/j.compstruct.2021.114312
26. Liu Y. et al. (2020), Three-dimensional fractal structure with double negative and density-near-zero properties on a subwavelength scale, Materials and Design, 188: 108470, https://doi.org/10.1016/j.matdes.2020.108470
27. Liu Z. et al. (2000), Locally resonant sonic materials, Science, 289(5485): 1734–1736, https://doi.org/10.1126/science.289.5485.1734
28. Long H. et al. (2020), Subwavelength broadband sound absorber based on a composite metasurface, Scientific Reports, 10(1): 1–10, https://doi.org/10.1038/s41598-020-70714-7
29. Long M. (2014), Sound transmission loss, [in:] Architectural Acoustics, 2nd ed., pp. 345–382, Boston: Academic Press, https://doi.org/10.1016/b978-0-12-398258-2.00009-x
30. Mahesh N.R., Prita N. (2011), Experimental and theoretical investigation of acoustic metamaterial with negative bulk modulus, Proceedings of 2011 COMSOL Conference, https://www.comsol.com/paper/experimental-and-theoretical-investigation-of-acoustic-metamaterial-with-negativ-11440
31. Naify C.J., Ikei A., Rohde C.A. (2020), Locally programmable metamaterial elements using fourdimensional printing, Extreme Mechanics Letters, 36: 100654, https://doi.org/10.1016/j.eml.2020.100654
32. Nicolas L., Furstoss M., Galland M.A. (1998), Analogy electromagnetism-acoustics: Validation and application to local impedance active control for sound absorption, EPJ Applied Physics, 4(1): 95–100, https://doi.org/10.1051/epjap%3A1998247
33. Ning S., Yan Z., Chu D., Jiang H., Liu Z., Zhuang Z. (2021), Ultralow-frequency tunable acoustic metamaterials through tuning gauge pressure and gas temperature, Extreme Mechanics Letters, 44: 101218, https://doi.org/10.1016/j.eml.2021.101218
34. Pendry J.B. (2000), Negative refraction makes a perfect lens, Physical Review Letters, 85(18): 3966–3969, https://doi.org/10.1103/PhysRevLett.85.3966
35. Pendry J.B., Schurig D., Smith D.R. (2006), Controlling electromagnetic fields, Science, 312(1780): 1780–1782, https://doi.org/10.1126/science.1125907
36. Peng Y.G., Shen Y.X., Geng Z.G., Li P.Q., Zhu J., Zhu X.F. (2020), Super-resolution acoustic image montage via a biaxial metamaterial lens, Science Bulletin, 65(12): 1022–1029, https://doi.org/10.1016/j.scib.2020.03.018
37. 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
38. Sang Hoon K., Mukunda D. (2012), Seismic waveguide of metamaterials, Modern Physics Letters B, 26(17): 1250105, https://doi.org/10.1142/S0217984912501059
39. Sarvazyan A.P., Urban M.W., Greenleaf J.F. (2013), Acoustic waves in medical imaging and diagnostics, Ultrasound in Medicine and Biology, 39(7): 1133–1146, https://doi.org/10.1016/j.ultrasmedbio.2013.02.006
40. Shao C., Long H., Cheng Y., Liu X. (2019), Low-frequency perfect sound absorption achieved by a modulus-near-zero metamaterial, Scientific Reports, 9(1): 1–8, https://doi.org/10.1038/s41598-019-49982-5
41. Shao H., He H., Chen Y., Tan X., Chen G. (2020), A tunable metamaterial muffler with a membrane structure based on Helmholtz cavities, Applied Acoustics, 157: 107022, https://doi.org/10.1016/j.apacoust.2019.107022
42. Sirota L., Sabsovich D., Lahini Y., Ilan R., Shokef Y. (2021), Real-time steering of curved sound beams in a feedback-based topological acoustic metamaterial, Mechanical Systems and Signal Processing, 153: 107479, https://doi.org/10.1016/j.ymssp.2020.107479
43. Smith D.R., Padilla W.J., Vier D.C., Nemat-Nasser S.C., Schultz S. (2000), Composite medium with simultaneously negative permeability and permittivity, Physical Review Letters, 84(18): 4184–4187, https://doi.org/10.1103/PhysRevLett.84.4184
44. Veselago V.G. (1968), The electrodynamic of substances with simultaneous negative values of ε and μ, Soviet Physics Uspekhi, 10(4): 509–514, https://doi.org/10.1070/pu1968v010n04abeh003699
45. Walser R.M. (2001), Electromagnetic metamaterials, [in:] Complex Mediums II: Beyond Linear Isotropic Dielectrics, A. Lakhtakia, W.S. Weiglhofer, I.J. Hodgkinson [Eds], Vol. 4467, SPIE, https://doi.org/10.1117/12.432921
46. Xiao S. et al. (2015), Active control of membrane-type acoustic metamaterial by electric field, Applied Physics Letters, 106(9): 091904, https://doi.org/10.1063/1.4913999
47. Yang M., Ma G., Yang Z., Sheng P. (2013), Coupled membranes with doubly negative mass density and bulk modulus, Physical Review Letters, 110(13): 134301, https://doi.org/10.1103/PhysRevLett.110.134301
48. Yang Z., Mei J., Yang M., Chan N.H., Sheng P. (2008), Membrane-type acoustic metamaterial with negative dynamic mass, Physical Review Letters, 101(20): 1–4, https://doi.org/10.1103/PhysRevLett.101.204301
49. Zangeneh-Nejad F., Fleury R. (2019), Active times for acoustic metamaterials, Reviews in Physics, 4:100031, https://doi.org/10.1016/j.revip.2019.100031
50. Zhang H., Xiao Y., Wen J., Yu D., Wen X. (2016), Ultra-thin smart acoustic metasurface for lowfrequency sound insulation, Applied Physics Letters, 108(14): 141902, https://doi.org/10.1063/1.4945664
51. Zhang S. (2010), Acoustic metamaterial design and applications, Ph.D. Dissertation, Graduate College of the University of Illinois, http://hdl.handle.net/2142/16524
52. Zhang X., Qu Z.,Wang H. (2020), Engineering acoustic metamaterials for sound absorption: from uniform to gradient structures, iScience, 23(5): 101110, https://doi.org/10.1016/j.isci.2020.101110
53. Zielinski T.G. et al. (2020), Reproducibility of soundabsorbing periodic porous materials using additive manufacturing technologies: round robin study, Additive Manufacturing, 36: 101564, https://doi.org/10.1016/j.addma.2020.101564
54. Zigoneanu L., Popa B., Cummer S.A. (2014), Three-dimensional broadband omnidirectional acoustic ground cloak, Nature Materials, 13(4): 352–355, https://doi.org/10.1038/NMAT3901
55. Ziolkowski R.W. (2014), Metamaterials: The early years in the USA, EPJ Applied Metamaterials, 1: 5, https://doi.org/10.1051/epjam/2014004
