ELASTIC WAVE PROPAGATION CHARACTERISTICS OF DENSITY GRADIENT CYLINDRICAL SHELL CHAINS

Peng Kefeng; Zheng Zhijun; Zhou Fenghua; Yu Jilin

doi:10.6052/0459-1879-22-019

Volume 54 Issue 8

Aug. 2022

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Chinese Journal of Theoretical and Applied Mechanics > 2022 > 54(8): 2131-2139. > DOI: 10.6052/0459-1879-22-019 CSTR: 32045.14.0459-1879-22-019

Peng Kefeng, Zheng Zhijun, Zhou Fenghua, Yu Jilin. Elastic wave propagation characteristics of density gradient cylindrical shell chains. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(8): 2131-2139. DOI: 10.6052/0459-1879-22-019

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ELASTIC WAVE PROPAGATION CHARACTERISTICS OF DENSITY GRADIENT CYLINDRICAL SHELL CHAINS

*.
CAS Key Laboratory of Mechanical Behavior and Design of Materials, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027, China
†.
MOE Key Laboratory of Impact and Safety Engineering, Faculty of Mechanical Engineering and Mechanics, Ningbo University, Ningbo 315211, Zhejiang, China

Received Date: January 05, 2022
Accepted Date: April 13, 2022
Available Online: April 14, 2022

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Abstract

Abstract

Uniform cylindrical shell chains can control elastic wave transmission, and introducing density gradient may further improve the ability of waveform control. The propagation behavior of elastic waves in the density gradient cylindrical shell chains was studied by developing a mesoscale finite element model and a continuum-based model. By equivalent the density gradient cylindrical shell chain to a variable density elastic rod, the governing equation of the density gradient chains under a stress pulse excitation was established. Based on the Laplace integral transformation and considering the linear density distribution in the rod, the analytical solution of the equation was obtained. Compared with the meso-finite element simulation results, it is found that the analytical solution can well predict the force evolution trend of the graded cylindrical shell chain under the excitation of a triangular stress pulse. The results show that the peak force in the positive gradient chain gradually increases with the wave propagation, while that of the negative gradient chain gradually decreases with the wave propagation. The peak force at the support end of the negative gradient chain is smaller than that of the uniform chain, while that of the positive gradient chain is greater than that of the uniform one. So the waveform control ability of the density gradient cylindrical shell chains is better than the uniform chain. The linear density gradient parameter has great influence on the waveform control ability of the density gradient cylindrical shell chains. The peak force transmitted to the support end increases with the increase of the density gradient parameter, and thus the density gradient cylindrical shell chain can control the stress pulse in a wider range. The theoretical model and its analytical solution provide a theoretical basis for studying the stress wave propagation law and revealing the force regulation mechanism of the graded cylindrical shell chains.
- waveform control,
- graded cylindrical shell chains,
- stress pulse excitation,
- continuum model,
- analytical solution

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References

[1]	Duan Y, Ding Y, Liu ZY, et al. Effects of cell size vs cell-wall thickness gradients on compressive behavior of additively manufactured foams. Composites Science and Technology, 2020, 199: 108339
[2]	Meng ZQ, Liu MC, Zhang YF, et al. Multi-step deformation mechanical metamaterials. Journal of the Mechanics and Physics of Solids, 2020, 144: 104095 doi: 10.1016/j.jmps.2020.104095
[3]	Peng KF, Zheng ZJ, Chang BX, et al. Wide-range control of impulse transmission by cylindrical shell chains with varying aspect ratios. International Journal of Impact Engineering, 2021, 158: 104017 doi: 10.1016/j.ijimpeng.2021.104017
[4]	Karagiozova D, Alves M. Stress waves in layered cellular materials—Dynamic compaction under axial impact. International Journal of Mechanical Sciences, 2015, 101: 196-213
[5]	Tang F, Sun Y, Guo Z, et al. Dynamic responses and energy absorption of hollow sphere structure subjected to blast loading. Materials & Design, 2019, 181: 107920
[6]	Wang SL, Ding YY, Yu F, et al. Crushing behavior and deformation mechanism of additively manufactured Voronoi-based random open-cell polymer foams. Materials Today Communications, 2020, 25: 101406 doi: 10.1016/j.mtcomm.2020.101406
[7]	Shim VPW, Guo YB, Lan R. Elastic stress transmission in cellular systems—Analysis of wave propagation. International Journal of Impact Engineering, 2008, 35(8): 845-869 doi: 10.1016/j.ijimpeng.2008.01.001
[8]	Zheng ZJ, Wang CF, Yu JL, et al. Dynamic stress–strain states for metal foams using a 3D cellular model. Journal of the Mechanics and Physics of Solids, 2014, 72: 93-114 doi: 10.1016/j.jmps.2014.07.013
[9]	Zhou H, Wang X, Zhao Z. High velocity impact mitigation with gradient cellular solids. Composites Part B: Engineering, 2016, 85: 93-101 doi: 10.1016/j.compositesb.2015.09.042
[10]	Valencia C, Restrepo D, Mankame ND, et al. Computational characterization of the wave propagation behavior of multi-stable periodic cellular materials. Extreme Mechanics Letters, 2019, 33: 100565 doi: 10.1016/j.eml.2019.100565
[11]	Zhang W, Xu J. Tunable traveling wave properties in one-dimensional chains composed from hollow cylinders: From compression to rarefaction waves. International Journal of Mechanical Sciences, 2021, 191: 106073 doi: 10.1016/j.ijmecsci.2020.106073
[12]	Gibson LJ, Ashby MF. Cellular Solids: Structure and Properties, Cambridge University Press, 1999
[13]	Wang SL, Zheng ZJ, Zhu CF, et al. Crushing and densification of rapid prototyping polylactide foam: Meso-structural effect and a statistical constitutive model. Mechanics of Materials, 2018, 127: 65-76 doi: 10.1016/j.mechmat.2018.09.003
[14]	Roberts AP, Garboczi EJ. Elastic moduli of model random three-dimensional closed-cell cellular solids. Acta Materialia, 2001, 49(2): 189-197 doi: 10.1016/S1359-6454(00)00314-1
[15]	Gibson IJ, Ashby MF. The mechanics of three-dimensional cellular materials. Proceedings of the Royal Society of London. A. Mathematical Physical Sciences, 1982, 382(1782): 43-59 doi: 10.1098/rspa.1982.0088
[16]	Cuan-Urquizo E, Shalchy F, Bhaskar A. Compressive stiffness of staggered woodpile lattices: Mechanics, measurement, and scaling laws. International Journal of Mechanical Sciences, 2020, 187: 105932 doi: 10.1016/j.ijmecsci.2020.105932
[17]	Yin S, Chen DH, Xu J. Novel propagation behavior of impact stress wave in one-dimensional hollow spherical structures. International Journal of Impact Engineering, 2019, 134: 103368 doi: 10.1016/j.ijimpeng.2019.103368
[18]	Wang XK, Zheng ZJ, Yu JL. Crashworthiness design of density-graded cellular metals. Theoretical and Applied Mechanics Letters, 2013, 3(3): 031001 doi: 10.1063/2.1303101
[19]	Chang BX, Zheng ZJ, Zhang YL, et al. Crashworthiness design of graded cellular materials: An asymptotic solution considering loading rate sensitivity. International Journal of Impact Engineering, 2020, 143: 103611 doi: 10.1016/j.ijimpeng.2020.103611
[20]	Yang J, Wang SL, Ding YY, et al. Crashworthiness of graded cellular materials: A design strategy based on a nonlinear plastic shock model. Materials Science and Engineering A, 2017, 680: 411-420 doi: 10.1016/j.msea.2016.11.010
[21]	Chaunsali R, Toles M, Yang J, et al. Extreme control of impulse transmission by cylinder-based nonlinear phononic crystals. Journal of the Mechanics and Physics of Solids, 2017, 107: 21-32 doi: 10.1016/j.jmps.2017.06.015
[22]	Kim H, Kim E, Chong C, et al. Demonstration of dispersive rarefaction shocks in hollow elliptical cylinder chains. Physical Review Letters, 2018, 120(19): 194101 doi: 10.1103/PhysRevLett.120.194101
[23]	Kim H, Kim E, Yang J. Nonlinear wave propagation in 3 D-printed graded lattices of hollow elliptical cylinders. Journal of the Mechanics and Physics of Solids, 2019, 125: 774-784 doi: 10.1016/j.jmps.2019.02.001
[24]	王礼立. 应力波基础, 第2版. 北京: 国防工业出版社, 2005 Wang Lili. Foundation of Stress Waves, 2nd edition. Beijing: National Defense Industry Press, 2005 (in Chinese)
[25]	彭克锋, 崔世堂, 潘昊等. 冲击载荷作用下柱壳链中的弹性波传播简化模型及其解析解. 爆炸与冲击, 2021, 41(1): 011403 doi: 10.11883/bzycj-2020-0246 Peng Kefeng, Cui Shitang, Pan Hao, et al. Simplified model of elastic wave propagation in cylindrical shell chain under impact load and its analytical solution. Explosion and Shock Waves, 2021, 41(1): 011403 (in Chinese) doi: 10.11883/bzycj-2020-0246
[26]	王礼立, 王永刚. 应力波在用SHPB研究材料动态本构特性中的重要作用. 爆炸与冲击, 2005, 25(01): 17-25 doi: 10.3321/j.issn:1001-1455.2005.01.004 Wang Lili, Wang Yonggang. The important role of stress waves in the study on dynamic constitutive behavior of materials by SHPB. Explosion and Shock Waves, 2005, 25(01): 17-25 (in Chinese) doi: 10.3321/j.issn:1001-1455.2005.01.004
[27]	Yang HS, Li YL, Zhou FH. Propagation of stress pulses in a Rayleigh-Love elastic rod. International Journal of Impact Engineering, 2021, 153: 103854 doi: 10.1016/j.ijimpeng.2021.103854
[28]	Bao RH, Yu TX. Impact and rebound of an elastic–plastic ring on a rigid target. International Journal of Mechanical Sciences, 2015, 91: 55-63 doi: 10.1016/j.ijmecsci.2014.03.031
[29]	Timoshenko SPG, James M. Theory of Elastic Stability, 2nd edition. Dover Publications, 2009
[30]	杨洪升, 李玉龙, 周风华. 梯形应力脉冲在弹性杆中的传播过程和几何弥散. 力学学报, 2019, 51(6): 1820-1829 doi: 10.6052/0459-1879-19-183 Yang Hongsheng, Li Yulong, Zhou Fenghua. The propagation process and the geometric dispersion of trapezoidal stress pulses in elastic rods. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(6): 1820-1829 (in Chinese) doi: 10.6052/0459-1879-19-183

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ELASTIC WAVE PROPAGATION CHARACTERISTICS OF DENSITY GRADIENT CYLINDRICAL SHELL CHAINS