Characteristic Research of Low Frequency Band Gaps and Structural Improvement in Single-Sided Column Local Resonance Phononic Crystals

Abstract

Abstract: Based on the finite element method, the band gap of the phononic crystal in single-sided cylinder local resonance was analyzed, and the influence of structural parameters on the phononic crystal was studied. The results show that the initial frequency of the first complete band gap decreases and the bandwidth increases with the increase of the height of the scatterer. With the increase of the thickness of the substrate, the initial frequency of the single-sided cylindrical phononic crystal increases gradually, the cut-off frequency first increases and then decreases. In addition, based on the classical single-sided cylindrical phononic crystal, two new ternary single-sided cylindrical phononic crystal structures are combined: embedded single-sided cylindrical phononic crystal (Hereinafter referred to as structure Ⅰ) and bonded single-sided cylindrical phononic crystal (Hereinafter referred to as structure Ⅱ). Through the analysis of the band gap characteristics, it is concluded that the two new structures have lower frequency band gap compared with the classical single-sided cylindrical phononic crystals, which is very beneficial for low-frequency vibration and noise reduction. The results of this paper will provide some theoretical guidance for practical engineering application.

Key words: single-sided cylindrical phononic crystal, finite element method, scatterer, band gap, low-frequency vibration and noise reduction

CLC Number:

O735

SUN Xiangyang, YAN Qun, GUO Xiangying. Characteristic Research of Low Frequency Band Gaps and Structural Improvement in Single-Sided Column Local Resonance Phononic Crystals[J]. Journal of Synthetic Crystals, 2021, 50(7): 1378-1385.

References

[1] ALY A H, NAGATY A, KHALIFA Z. Piezoelectric material and one-dimensional phononic crystal[J]. Surface Review and Letters, 2019, 26(2): 1850144.
[2] KRIEGEL I, SCOTOGNELLA F, MANNA L. Plasmonic doped semiconductor nanocrystals: properties, fabrication, applications and perspectives[J]. Physics Reports, 2017, 674: 1-52.
[3] WU F G, HOU Z L, LIU Z Y, et al. Point defect states in two-dimensional phononic crystals[J]. Physics Letters A, 2001, 292(3): 198-202.
[4] 温熙森,温激泓,郁殿龙.声子晶体[M].北京:国防工业出版社,2009.
WEN X S, WEN J H, YU D L. Phononic crystal[M]. Beijing: National Defense Industry Press, 2009(in Chinese).
[5] WU X D, SUN L Z, ZUO S G, et al. Transfer path analysis and low-frequency vibration reduction by locally resonantphononic crystal[C]//SAE Technical Paper Series. 400 Commonwealth Drive, Warrendale, PA, United States: SAE International, 2019-01-0786.
[6] HE H, SHAO H B, HE C, et al. Study on the band gap optimization and defect state of two-dimensional honeycomb phononic crystals[J]. Journal of Materials Research, 2020, 35(21): 3021-3030.
[7] 陈鑫,姚宏,赵静波,等.双局域共振Helmholtz声子晶体带隙研究[J].人工晶体学报,2019,48(1):13-17.
CHEN X, YAO H, ZHAO J B, et al. Study on the bandgap of double local resonance Helmholtz phononic crystals[J]. Journal of Synthetic Crystals, 2019, 48(1): 13-17(in Chinese).
[8] ZHAI H F, XIANG H, MA X F, et al. Optimal bandgaps of a spiral structure based on locally resonant phononic crystals[J]. International Journal of Modern Physics B, 2019, 33(22): 1950256.
[9] 董亚科,杜军,姚宏,等.双包覆层局域共振型声子晶体带隙特性研究[J].人工晶体学报,2015,44(12):3676-3680.
DONG Y K, DU J, YAO H, et al. Study on band gap characteristics ofphononic crystal composed by double coated layer[J]. Journal of Synthetic Crystals, 2015, 44(12): 3676-3680(in Chinese).
[10] WANG X P, JIANG P, CHEN T N, et al. Tuning characteristic of band gap and waveguide in a multi-stub locally resonant phononic crystal plate[J]. AIP Advances, 2015, 5(10): 107141.
[11] XU K, LI Z, ZHANG Y L, et al. An indirect approach based on Clausius-Clapeyron equation to determine entropy change for the first-order magnetocaloric materials[J]. Physics Letters A, 2015, 379(47/48): 3149-3154.
[12] ZHANG G M, ZHAO L B, JIANG Z D, et al. Surface stress-induced deflection of a microcantilever with various widths and overall microcantilever sensitivity enhancement via geometry modification[J]. Journal of Physics D: Applied Physics, 2011, 44(42): 425402.
[13] WANG Y F, WANG Y S. Complete bandgaps in two-dimensional phononic crystal slabs with resonators[J]. Journal of Applied Physics, 2013, 114(4): 043509.
[14] JIN Y B, TORRENT D, PENNEC Y, et al. Simultaneous control of the S0 and A0 Lamb modes by graded phononic crystal plates[J]. Journal of Applied Physics, 2015, 117(24): 244904.
[15] BENCHABANE S, GAIFFE O, SALUT R, et al. Guidance of surface waves in a micron-scale phononic crystal line-defect waveguide[J]. Applied Physics Letters, 2015, 106(8): 081903.
[16] 郭翔鹰,孙向洋,朱雨男.二维正方晶格钨-硅橡胶声子晶体的带隙特性研究[J].人工晶体学报,2020,49(9):1583-1589.
GUO X Y, SUN X Y, ZHU Y N. Characteristic of bandgaps in two-dimensional ternary lattice tungsten-silicone rubberphononic crystals[J]. Journal of Synthetic Crystals, 2020, 49(9): 1583-1589(in Chinese).
[17] GOFFAUX C, SÁNCHEZ-DEHESA J, YEYATI A L, et al. Evidence of fano-like interference phenomena in locally resonant materials[J]. Physical Review Letters, 2002, 88(22): 225502.
[18] GU Y W, LUO X D, MA H R. Low frequency elastic wave propagation in two dimensional locally resonant phononic crystal with asymmetric resonator[J]. Journal of Applied Physics, 2009, 105(4): 044903.
[19] YAO Y W, WU F G, ZHANG X, et al. Lamb wave band gaps in locally resonant phononic crystal strip waveguides[J]. Physics Letters A, 2012, 376(4): 579-583.
[20] WANG G, WEN X, WEN J, et al. Two-dimensional locally resonant phononic crystals with binary structures[J]. Physical Review Letters, 2004, 93(15): 154302.
[21] HSU J C, WU T T. Lamb waves in binary locally resonant phononic plates with two-dimensional lattices[J]. Applied Physics Letters, 2007, 90(20): 201904.
[22] QI X Q, LI T J, ZHANG J L, et al. Band gap structures for 2D phononic crystals with composite scatterer[J]. Applied Physics A, 2018, 124(5): 1-7.
[23] BAGHERI NOURI M, MORADI M. Presentation and investigation of a new two dimensional heterostructure phononic crystal to obtain extended band gap[J]. Physica B: Condensed Matter, 2016, 489: 28-32.
[24] QIAN D H. Wave propagation in a thermo-magneto-mechanical phononic crystal nanobeam with surface effects[J]. Journal of Materials Science, 2019, 54(6): 4766-4779.
[25] MORADI P, BAHRAMI A. Design of an optomechanical filter based on solid/solid phoxonic crystals[J]. Journal of Applied Physics, 2018, 123(11): 115113.
[26] XU Z, XU W, QIAN M L, et al. A flat acoustic lens to generate a Bessel-like beam[J]. Ultrasonics, 2017, 80: 66-71.
[27] YAO L Y, HUANG G L, CHEN H, et al. A modified smoothed finite element method (M-SFEM) for analyzing the band gap in phononic crystals[J]. Acta Mechanica, 2019, 230(6): 2279-2293.
[28] 张昭,苏开创,韩星凯.单面柱声子晶体板低频带隙特性与机理分析[J].计算机辅助工程,2016,25(5):46-52.
ZHANG Z, SU K C, HAN X K. Low frequency band gap property and mechanism analysis ofphononic crystal plate with one-sided columns[J]. Computer Aided Engineering, 2016, 25(5): 46-52(in Chinese).