Propagation Band Gap Characteristics of Open Ring-Like Phononic Crystal

Abstract

Abstract: In order to attenuate the mid- and low-frequency vibration noise, a non-strictly symmetrical open ring-like phononic crystal structure was designed. Based on the finite element method and elastic wave theory, its band gap characteristics and vibration attenuation performance in various directions were analyzed; Combined with the vibration mode of the system, the reasons for the opening and closing of the band gap were explained, and the influence of geometric parameters on the band gap width was analyzed. The results show that due to the non-strict symmetry of the crystal, only the transmission loss in the ΓX direction is consistent with the band gap characteristics, and the attenuation performance is better than that in the MΓ direction. The average attenuation in the band gap is 27.8 dB, which is 5.5 dB higher than that in the MΓ direction. There is almost no displacement deformation in the forbidden band, and the deformation of the pass band significantly increases due to the inability to suppress the propagation of elastic waves; the horizontal and rotational movement of the core is an obvious sign of the beginning and end of the band gap. With tungsten as the core, the starting frequency and bandwidth are 500 Hz. Increasing the material density, filling rate and lattice size of the core will help to obtain a complete band gap at lower frequencies.

Key words: ring-like phononic crystal, band gap structure, directional transmission loss, geometric size, vibration attenuation performance

CLC Number:

O735

TANG Rongjiang, PAN Chaoyuan, ZHENG Weiguang, HE Hongbin, TANG Jingtian. Propagation Band Gap Characteristics of Open Ring-Like Phononic Crystal[J]. Journal of Synthetic Crystals, 2021, 50(3): 428-434.

References

[1] 蒋娟娜,姚宏,赵静波,等.多重开孔式声子晶体隔声特性研究[J].人工晶体学报,2019,48(3):379-385.
JIANGJ N, YAO H, ZHAO J B, et al.Sound isolation characteristics of phononic crystal with multi-opening structure[J]. Journal of Synthetic Crystals, 2019, 48(3): 379-385(in Chinese).
[2] 麻乘榕,邵晨,万庆冕,等.用于汽车低频振动控制的局域共振声子晶体[J].应用声学,2018,37(1):152-158.
MA C R, SHAO C, WAN Q M, et al.A locally-resonant phononic crystal for low-frequency vibration control of vehicles[J]. Journal of Applied Acoustics, 2018, 37(1): 152-158(in Chinese).
[3] ELFORD D P, CHALMERS L, KUSMARTSEV F V, et al.Matryoshka locally resonant sonic crystal[J]. The Journal of the Acoustical Society of America, 2011, 130(5): 2746-2755.
[4] YU K P, CHEN T N, WANG X P.Large band gaps in two-dimensional phononic crystals with neck structures[J]. Journal of Applied Physics, 2013, 113(13): 134901.
[5] 姜久龙,姚宏,杜军,等.双开口Helmholtz局域共振周期结构低频带隙特性研究[J].物理学报,2017,66(6):136-142.
JIANG J L, YAO H, DU J, et al.Low frequency band gap characteristics of double-split Helmholtz locally resonant periodic structures[J]. Acta Physica Sinica, 2017, 66(6): 136-142(in Chinese).
[6] 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).
[7] 祁鹏山,杜军,姜久龙,等.二维声子晶体的隔声机理及其特性[J].硅酸盐学报,2016,44(10):1458-1464.
QI P S, DU J, JIANG J L, et al.Transmission loss mechanism and characteristics of two-dimensional phononic crystals[J]. Journal of the Chinese Ceramic Society, 2016, 44(10): 1458-1464(in Chinese).
[8] WANG Y F, WANG Y S, SU X X.Large bandgaps of two-dimensional phononic crystals with cross-like holes[J]. Journal of Applied Physics, 2011, 110(11): 113520.
[9] 严珠妹,赵寰宇,汪越胜.含旋转对称性孔的二维声子晶体带隙特性研究[J].人工晶体学报,2015,44(9):2443-2449.
YANZ M, ZHAO H Y, WANG Y S.Properties of elastic waves bandgaps in two-dimensional phononic crystals with rotational symmetry holes[J]. Journal of Synthetic Crystals, 2015, 44(9): 2443-2449(in Chinese).
[10] COLLET M, OUISSE M, RUZZENE M, et al.Floquet-Bloch decomposition for the computation of dispersion of two-dimensional periodic, damped mechanical systems[J]. International Journal of Solids and Structures, 2011, 48(20): 2837-2848.
[11] PALERMO A, MARZANI A. A reduced Bloch operator finite element method for fast calculation of elastic complex band structures[J]. International Journal of Solids and Structures, 2020, 191/192: 601-613.
[12] COMSOL. Solid mechanics module user’s guide[M]. Sweden: Stockholm.
[13] XU Y L, CHEN C Q, TIAN X G.Wave characteristics of two-dimensional hierarchical hexagonal lattice structures[J]. Journal of Vibration and Acoustics, 2014, 136(1): 011011. DOI:10.1115/1.4025550.
[14] 吴九汇,张思文,沈礼.螺旋局域共振单元声子晶体板结构的低频振动带隙特性研究[J].机械工程学报,2013,49(10):62-69.
WU J H, ZHANG S W, SHEN L.Low-frequency vibration characteristics of periodic spiral resonators in phononic crystal plates[J]. Journal of Mechanical Engineering, 2013, 49(10): 62-69(in Chinese).
[15] 王刚. 声子晶体局域共振带隙机理及减振特性研究[D].长沙:国防科学技术大学,2005.
WANG G.Research on the mechanism and the vibration attenuation characteristic of locally resonant band gap in phononic crystals[D]. Changsha: National University of Defense Technology, 2005(in Chinese).