Low-Frequency Band Gap Characteristics of Phononic Crystal of One-Resonator and One-Resonator with Elastic Support

Abstract

Abstract: Local resonance phononic crystals can be constructed by adding resonance elements periodically, and low frequency band gap can be generated. In this paper, a phononic crystal composed of one-resonator and one-resonator with elastic support has been presented. The band gap characteristics and band gap regulation characteristics of the structure were calculated and analyzed by using phononic crystal theory and vibration theory. The results show that the initial frequency of the first band gap is 0 Hz. The attenuation of vibration in the band gap is determined by the attenuation factor and period number of the finite structure. There are one tunable band gap and three untunable band gaps in such structure. By changing the structural parameters of one-resonator and one-resonator with elastic support, the tunable band gap can be tuned. The untuable band gaps which include the first band gap can attenuate elastic wave stably. The band gap characteristics of the structure have potential applications in the field of vibration reduction of pipelines, bridges and automobiles.

Key words: phononic crystal, low-frequency band gap, complex band structure, band gap tunable, one-resonator, elastic support

CLC Number:

TB123

LI Jing, WANG Hongsai, GUAN Dong, ZHANG Chun, SHEN Hui. Low-Frequency Band Gap Characteristics of Phononic Crystal of One-Resonator and One-Resonator with Elastic Support[J]. Journal of Synthetic Crystals, 2021, 50(1): 7-12.

References

[1] GAO N, WEI Z, HOU H, et al. Design and experimental investigation of V-folded beams with acoustic black hole indentations[J]. The Journal of the Acoustical Society of America, 2019, 145(1):EL79-83.
[2] 梁孝东,缪林昌,尤佺,等.局域共振二维声子晶体的低频带隙特性研究[J].人工晶体学报,2019,48(7):1225-1232.
LIANG X D, MIAO L C, YOU Q, et al. Low-frequency band gap characteristics of locally resonant two-dimensional phononic crystal[J]. Journal of Synthetic Crystals, 2019, 48(7): 1225-1232(in Chinese).
[3] MA F, CHEN J, WU J H. Three-dimensional acoustic sub-diffraction focusing by coiled metamaterials with strong absorption[J]. Journal of Materials Chemistry C, 2019, 17(7): 5131-5138.
[4] LIU C, WU J H, CHEN X, et al. A thin low-frequency broadband metasurface with multi-order sound absorption[J]. Journal of Physics D, 2019, 52(10): 105302.
[5] KUSHWAHA M S, HALEVI P, DOBRZYNSKI L, et al. Acoustic band structure of periodic elastic composites[J]. Physical Review Letters, 1993, 71(13): 2022-2025.
[6] LIU Z, ZHANG X, MAO Y, et al. Locally resonant sonic materials[J]. Science, 2000, 289(5485): 1734-1736.
[7] 温激鸿,刘耀宗,郁殿龙,等.基于散射单元的声子晶体振动带隙研究[J].人工晶体学报,2004,33(3):358-362.
WEN J H, LIU Y Z, YU D L, et al. Research on vibration band gaps of phononic crystals consisting of scattering cells[J]. Journal of Synthetic Crystals, 2004, 33(3): 358-362(in Chinese).
[8] 许振龙,吴福根,郭钟宁.基于声子晶体环形腔的可调声波分插滤波器[J].人工晶体学报,2016,45(9):2246-2250.
XU Z L, WU F G, GUO Z N. Tunable acoustic add-drop filter based on ring resonator of phononic crystals[J]. Journal of Synthetic Crystals, 2016, 45(9): 2246-2250(in Chinese).
[9] 郑忱煜,徐德辉,熊斌.基于微机械加工工艺的声子晶体器件[J].人工晶体学报,2019,48(8):1418-1423.
ZHENG C Y, XU D H, XIONG B. Phononic crystal devices based on micromachining technology[J]. Journal of Synthetic Crystals, 2019, 48(8): 1418-1423(in Chinese).
[10] JENSEN J S. Phononic band gaps and vibrations in one-and two-dimensional mass-spring structures[J]. Journal of Sound and Vibration, 2003, 266(5): 1053-1078.
[11] JING L, WU J H, GUAN D, et al. Multilayer-split-tube resonators with low-frequency band gaps in phononic crystals[J]. Journal of Applied Physics, 2014, 116(10): 103514.
[12] YAO S, ZHOU X, HU G. Experimental study on negative effective mass in a 1D mass-spring system[J]. New Journal of Physics, 2008, 10(4): 043020.
[13] HUANG H H, SUN C T, HUANG G L. On the negative effective mass density in acoustic metamaterials[J]. International Journal of Engineering Science, 2009, 47(4): 610-617.
[14] HUANG G L, SUN C T. Band gaps in a multiresonator acoustic metamaterial[J]. Journal of Vibration and Acoustics, 2010, 132(3): 031003.
[15] LI Q Q, HE Z C, LI E. Dissipative multi-resonator acoustic metamaterials for impact force mitigation and collision energy absorption[J]. Acta Mechanica, 2019, 230: 2905-2935.
[16] ALAMRI S, LI B, TAN K T. Dynamic load mitigation using dissipative elastic metamaterials with multiple Maxwell-type oscillators[J]. Journal of Applied Physics, 2018, 123(9): 095111.
[17] BARNHART M V, XU X, CHEN Y, et al. Experimental demonstration of a dissipative multi-resonator metamaterial for broadband elastic wave attenuation[J]. Journal of Sound and Vibration, 2019, 438: 1-12.
[18] NARISETTI R K, LEAMY M J, RUZZENE M. A perturbation approach for predicting wave propagation in one-dimensional nonlinear periodic structures[J]. Journal of Vibration and Acoustics, 2010, 132(3): 031001.
[19] YAO S, ZHOU X, HU G. Investigation of the negative-mass behaviors occurring below a cut-off frequency[J]. New Journal of Physics, 2010, 12(10): 103025.
[20] LIU Y, SU X, SUN C T. Broadband elastic metamaterial with single negativity by mimicking lattice systems[J]. Journal of the Mechanics and Physics of Solids, 2015, 74: 158-174.
[21] LEE S H, PARK C M, SEO Y M, et al. Acoustic metamaterial with negative density[J]. Physics letters A, 2009, 373(48): 4464-4469.
[22] LU K, WU J H, GUAN D, et al. A lightweight low-frequency sound insulation membrane-type acoustic metamaterial[J]. Aip Advances, 2016, 6(2): 025116.
[23] LI B, TAN K T. Asymmetric wave transmission in a diatomic acoustic/elastic metamaterial[J]. Journal of Applied Physics, 2016, 120(7): 075103.
[24] LIU Y, SHEN X, SU X, et al. Elastic metamaterials with low-frequency passbands based on lattice system with on-site potential[J]. Journal of Vibration and Acoustics, 2016, 138(2): 021011.
[25] LIU Y, YI J, LI Z, et al. Dissipative elastic metamaterial with a low-frequency passband[J]. AIP Advances, 2017, 7(6): 065215.