A study on the vibration band gap and vibration characteristics of a cylindrical shell phononic crystal

PDF(1026 KB)

Journal of Vibration and Shock ›› 2019, Vol. 38 ›› Issue (8) : 133-138.

LUO Jinyu，YAO Lingyun，JIANG Guoqi，WU Fei

Author information +

History +

Abstract

A cylindrical shell structure is widely used in structure design but its vibration noise problem commonly exists.Based on the theory of two-dimensional plate phononic crystal and the mechanism of Bragg scattering, this work presents a cylindrical shells phononic crystal model.According to the dynamic equation theory of cylindrical shell and Bloch periodic condition, the vibration characteristic of this structure was studied with an established finite element model.This research took a phononic crystal structure with a radius of 0.1m as an example, calculated its band structure, and analyzed its vibration characteristics.To verify the accuracy of the calculated band gap, the vibration transfer of cylinder shell models with multiple periodic structures was analyzed through the finite element method (FEM).The result shows that the vibration transfer function curve match the band gap well.It indicates that, similar to the plate structure, cylindrical shell phonon crystals also have quite good band gap and total forbidden band gap along the axial line and direction of cylinder ring.

Key words

Cylindrical shell / Phononic crystal / Band structure / Band gap / Vibration transfer

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations

LUO Jinyu，YAO Lingyun，JIANG Guoqi，WU Fei. A study on the vibration band gap and vibration characteristics of a cylindrical shell phononic crystal[J]. Journal of Vibration and Shock, 2019, 38(8): 133-138

References

[1] DEYMIER P A. Acoustic Metamaterials and Phononic Crystals [M]. Berlin Heidelberg: Springer-Verlag, 2013.
[2] 温熙森, 温激鸿, 郁殿龙, 等. 声子晶体 [M]. 北京：国防工业出版社, 2002.
Wen Xi-sen, Wen Ji-hong, Yu Dian-long, et al. Phononic Crystals [M]. Peking: National Defence Industry Press, 2002.
[3] SIGALAS M, ECONOMOU E N. Band structure of elastic waves in two dimensional systems [J]. Solid State Commun, 1993, 86(3): 141-143.
[4] KUSHWAHA M S, HALEVI P, MARTINEZ G, et al. Theory of acoustic band structure of periodic elastic composites [J]. Physical Review B Condensed Matter, 1994, 49(4): 2313-2322.
[5] 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.
[6] WU T T, HSU J C, SUN J H. Phononic plate waves [J]. Ultrasonics Symposium, 2011, 58(10): 2146-2161.
[7] LEE G Y, CHONG C, KEVREKIDIS P G, et al. Wave mixing in coupled phononic crystals via a variable stiffness mechanism [J]. Journal of the Mechanics and Physics of Solids, 2016, 95: 501-516.
[8] LIU Z, ZHANG X, MAO Y, et al. Locally resonant sonic materials [J]. SCIENCE, 2000, 289(5485): 1734-17366.
[9] 温激鸿. 声子晶体振动带隙及减振特性研究 [D]. 长沙：国防科技大学，2005.
Wen Ji-hong. Vibration Attenuation and Band Gap Characteristics of Phononic Crystals [D]. Changsha: National University of Defence Technology, 2005.
[10] LIU Z, CHAN C T, SHENG P. Three-component elastic wave band-gap material [J]. Physical Review B Condensed Matter, 2002, 65(16): 165116.
[11] ZHANG X, LIU Y, Wu F, et al. Large two-dimensional band gaps in three component phononic crystals [J]. Physics Letters A, 2003, 317(1): 144-149.
[12] 冯端, 金国均. 凝聚态物理学 [M]. 北京:高等教育出版社, 2013.
Feng Duan, Jin Guo-jun. Condensed matter physics [M]. Peking: Higher Education Press, 2013.
[13] JENSEN J. Phononic band gaps and vibrations in one- and two-dimensional mass-spring structures [J]. Journal of Sound & Vibration, 2003, 266(5): 1053-078.
[14] SONG Y, WEN J, YU D, et al. Reduction of vibration and noise radiation of an underwater vehicle due to propeller forces using periodically layered isolators [J]. Journal of Sound and Vibration, 2014, 333(14): 3031-3043.
[15] SHARMA B, SUN C T. Impact load mitigation in sandwich beams using local resonators [J]. Journal of sandwich structures & materials, 2016, 18: 50-64.
[16]赵浩江, 宋扬, 刘荣强. 轮辐板式局域共振声子晶体隔振器的振动特性研究 [J]. 振动与冲击, 2017, 36(15): 43-50.
Zhao Hao-jiang, Song Yang, Liu Rong-qiang. Vibration characteristics of spoke-like vibration isolators with locally resonant photonic crystal plates [J]. Journal of Vibration and Shock, 2017, 36(15): 43-50.
[17] HE Z C, XIAO X, LI E. Design for structural vibration suppression in laminate acoustic metamaterials [J]. Composites Part B: Engineering, 2017, 131: 237-252.
[18] 温激鸿, 郁殿龙, 王刚, 等. 周期结构细直梁弯曲振动中的振动带隙 [J]. 机械工程学报, 2005, 41(4): 1-6.
Wen Ji-hong, Yu Dian-long, Wang Gang, et al. Elastic wave band gaps in flexural vibrations of straight beams [J]. Chinese Journal of Mechanical Engineering, 2005, 41(4): 1-6.
[19] WANG M Y, WANG X. Frequency band structure of locally resonant periodic flexural beams suspended with force-moment resonators [J]. Journal of Physics D: Applied Physics, 2013, 46(46): 255502.
[20] 郁殿龙, 刘耀宗, 王刚, 等. 二维声子晶体薄板的振动特性[J]. 机械工程学报, 2006, 42(2): 150-154.
Yu Dian-long, Liu Yao-zong, Wang Gang, et al. Vibration property of two dimension phononic crystals thin plate [J]. Chinese Journal of Mechanical Engineering, 2006, 42(2): 150-154.
[21] SONG Y, FENG L, WEN J, et al. Analysis and enhancement of flexural wave stop bands in 2D periodic Plates [J]. Physics Letters A, 2015, 379: 1449-1456.
[22] DOYLE J F. Wave Propagation in Structures: Spectral Analysis Using Fast Discrete Fourier Transforms [M]. New York: Springer-Verlag, 1997.
[23] TYUTEKIN V. Helical waves of an elastic cylindrical shell [J]. Acoustical Physics, 2004, 50: 273-280.
[24] PANY C, PARTHAN S. Axial wave propagation in long periodic curved panels [J]. Journal of Vibration and Acoustics, 2003, 125: 24-30.
[25] MANCONI E, MACE B, Wave characterization of cylindrical and curved panels using a finite element method [J]. The Journal of Acoustical Society of America, 2009, 125(1): 154-163.
[26] NATEGHI A, VAN BELLE L, CLAEYS C, et al. Wave propagation in locally resonant cylindrically curved metamaterial panels [J]. International Journal of Mechanical Sciences, 2017, 127: 73-90.
[27] 谢宇晗，尹剑飞，温激鸿. 一种环布动力吸振器的圆柱壳声振控制设计 [J]. 噪声与振动控制，2018, 38(Z1): 264-268.
Xie Yu-han, Yin Jian-fei, Wen Ji-hong. Design of Vibro-acoustic Control of the Cylindrical Shell via a Dynamic Vibration Absorber Annulus [J]. Noise and Vibration Control, 2018, 38(Z1): 264-268.
[28] 黄昆. 固体物理学 [M]. 北京: 人民出版社,1979.
Huang Kun. Solid state physics [M]. Pekin: People’s Publishing House, 1979.