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

彭克锋; 崔世堂; 潘昊; 郑志军; 虞吉林

doi:10.11883/bzycj-2020-0246

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

doi: 10.11883/bzycj-2020-0246

1.
中国科学技术大学近代力学系中国科学院材料力学行为和设计重点实验室，安徽合肥 230027
2.
北京应用物理与计算数学研究所，北京 100088

基金项目: 国家自然科学基金(11772330, 11872360)；中央高校基本科研业务费专项(WK2480000003, WK2090050043)

详细信息

作者简介:
彭克锋（1994－　），男，博士研究生，pkf@mail.ustc.edu.cn

通讯作者:
郑志军（1979－　），男，副教授，zjzheng@ustc.edu.cn

中图分类号: O347.4
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- 被引次数: 0
出版历程
- 收稿日期: 2020-07-17
- 修回日期: 2020-08-31
- 刊出日期: 2021-01-05

Simplified model of elastic wave propagation in cylindrical shell chain under impact load and its analytical solution

1.
CAS Key Laboratory of Mechanical Behavior and Design of Materials, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027, Anhui, China
2.
Institute of Applied Physics and Computational Mathematics, Beijing 100088, China

摘要

摘要: 柱壳链能引起波形的弥散，具备操控波形的潜力。建立了柱壳链结构的等效连续介质模型和细观有限元模型，研究了质量块冲击作用下柱壳链中的弹性应力波传播过程及其几何弥散特性。基于考虑横向惯性修正的Rayleigh-Love波动方程，建立了柱壳链在质量块冲击下的控制方程，采用Laplace变换及其逆变换获得了位移场、速度场和应变场的解析解，所得结果与细观有限元模拟结果较好吻合。结果表明，在冲击过程中应变和速度峰值均逐渐减小，应变峰值、振荡幅度和波形前沿宽度与泊松比和惯性半径相关，泊松比和惯性半径越大，应变峰值越小，应变分布振荡越剧烈，波形前沿宽度越宽。
- 柱壳链 /
- 应力波 /
- 横向惯性修正 /
- 解析解 /
- 几何弥散
Abstract: Cylindrical shell chain can cause dispersion of waveform and has the potential to manipulate waveform. An equivalent continuum model and a mesoscopic finite element model of cylindrical shell chain structure were established, and the stress wave propagation process and its geometric dispersion characteristics in cylindrical shell chains under mass impact were studied. For the in-plane compression of a single cylindrical shell, the deformation in the out-of-plane direction is very small and the in-plane deformation perpendicular to the loading direction is relatively large. Thus, the out-of-plane Poisson’s ratio can be taken as 0, but the in-plane one cannot be ignored. For the simplification of analysis, the cylindrical shell chain is considered as a rod composed of anisotropic homogeneous continuum. Based on the Rayleigh-Love wave equation with the transverse inertia correction, the governing equation of elastic wave propagation in a cylindrical shell chain under mass impact was obtained and rewritten in a dimensionless form. The analytical solutions of displacement, velocity and strain fields were obtained by using Laplace transform and its inverse transform and expressed in the form of infinite series. A chain with 30 cylindrical shells was constructed numerically and its dynamic impact behavior was simulated with finite element code ABAQUS/Explicit. The theoretical predictions of mechanical responses are in good agreement with the results of mesoscopic finite element simulation. During the impact process, the peak values of strain and velocity decrease gradually. The peak strain, the oscillation amplitude of waveform and the width of waveform front are related to the in-plane Poisson's ratio and the radius of gyration of the cylindrical shell chain. The larger the in-plane Poisson's ratio and the radius of gyration of the cylindrical shell chain, the smaller the peak strain, the stronger the oscillation of the strain waveform and the wider the width of the waveform front.
- cylindrical shell chain /
- stress wave /
- transverse inertia correction /
- analytical solution /
- geometric dispersion

HTML全文

图 1 柱壳链简化模型

Figure 1. Simplified model of a cylindrical shell chain

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图 2 不同时刻柱壳链中的应力云图

Figure 2. Von Mises stress distributions in the cylindrical shell chain at different times

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图 3 名义应力应变曲线和等效泊松比

Figure 3. Nominal stress-strain curves and equivalent Poissons ratios

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图 4 冲击端的位移、冲击端和支撑端的载荷

Figure 4. Displacements at the support end, forces at the impact and support ends

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图 5 不同时刻杆中的应变和速度分布

Figure 5. Strain and velocity distributions in rod at different times

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图 6 不同冲击速度下杆中的应变分布

Figure 6. Strain distributions in rod under different impact velocities

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图 7 不同壁厚时杆中的应变分布

Figure 7. Strain distributions in rod with different wall thicknesses

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图 8 泊松比和惯性半径对应变分布的影响

Figure 8. Influences of Poisson’s ratio and inertia radius on strain distributions

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图 9 无量纲速度和无量纲质量对应变分布的影响

Figure 9. Influences of dimensionless velocity and mass on strain distributions

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参考文献(26)

[1]	JIANG S, SHEN L M, GUILLARD F, et al. Energy dissipation from two-glass-bead chains under impact [J]. International Journal of Impact Engineering, 2018, 114: 160–168. DOI: 10.1016/j.ijimpeng.2018.01.002.
[2]	KIM E, YANG J, HWANG H, et al. Impact and blast mitigation using locally resonant woodpile metamaterials [J]. International Journal of Impact Engineering, 2017, 101: 24–31. DOI: 10.1016/j.ijimpeng.2016.09.006.
[3]	PARK C M, PARK J J, LEE S H, et al. Amplification of acoustic evanescent waves using metamaterial slabs [J]. Physical Review Letters, 2011, 107(19): 194301. DOI: 10.1103/physrevlett.107.194301.
[4]	DONAHUE C M, ANZEL P W J, BONANOMI L, et al. Experimental realization of a nonlinear acoustic lens with a tunable focus [J]. Applied Physics Letters, 2014, 104(1): 014103. DOI: 10.1063/1.4857635.
[5]	TAN K T, HUANG H H, SUN C T. Blast-wave impact mitigation using negative effective mass density concept of elastic metamaterials [J]. International Journal of Impact Engineering, 2014, 64: 20–29. DOI: 10.1016/j.ijimpeng.2013.09.003.
[6]	DARAIO C, NESTERENKO V F, HERBOLD E B, et al. Energy trapping and shock disintegration in a composite granular medium [J]. Physical Review Letters, 2006, 96(5): 058002. DOI: 10.1103/physrevlett.96.058002.
[7]	LI F, ANZEL P, YANG J, et al. Granular acoustic switches and logic elements [J]. Nature Communications, 2014, 5(1): 5311. DOI: 10.1038/ncomms6311.
[8]	NESTERENKO V F. Propagation of nonlinear compression pulses in granular media [J]. Journal of Applied Mechanics and Technical Physics, 1983, 24(5): 733–743. DOI: 10.1007/bf00905892.
[9]	KIM H, KIM E, CHONG C, et al. Demonstration of dispersive rarefaction shocks in hollow elliptical cylinder chains [J]. Physical Review Letters, 2018, 120(19): 194101. DOI: 10.1103/physrevlett.120.194101.
[10]	NGO D, GRIFFITHS S, KHATRI D, et al. Highly nonlinear solitary waves in chains of hollow spherical particles [J]. Granular Matter, 2013, 15(2): 149–155. DOI: 10.1007/s10035-012-0377-5.
[11]	ON T, WANG E H, LAMBROS J. Plastic waves in one-dimensional heterogeneous granular chains under impact loading: Single intruders and dimer chains [J]. International Journal of Solids and Structures, 2015, 62: 81–90. DOI: 10.1016/j.ijsolstr.2015.02.006.
[12]	GANESH R, GONELLA S. Nonlinear waves in lattice materials: adaptively augmented directivity and functionality enhancement by modal mixing [J]. Journal of the Mechanics and Physics of Solids, 2017, 99: 272–288. DOI: 10.1016/j.jmps.2016.11.001.
[13]	YIN S, CHEN D H, XU J. Novel propagation behavior of impact stress wave in one-dimensional hollow spherical structures [J]. International Journal of Impact Engineering, 2019, 134: 103368. DOI: 10.1016/j.ijimpeng.2019.103368.
[14]	KIM H, KIM E, YANG J. Nonlinear wave propagation in 3D-printed graded lattices of hollow elliptical cylinders [J]. Journal of the Mechanics and Physics of Solids, 2019, 125: 774–784. DOI: 10.1016/j.jmps.2019.02.001.
[15]	JOHNSON K L. Contact mechanics [M]. Cambridge: Cambridge University Press, 1985.
[16]	PAUCHARD L, RICA S. Contact and compression of elastic spherical shells: the physics of a“ping-pong”ball [J]. Philosophical Magazine B, 1998, 78(2): 225–233. DOI: 10.1080/13642819808202945.
[17]	KIM E, YANG J. Review: wave propagation in granular metamaterials [J]. Functional Composites and Structures, 2019, 1(1): 012002. DOI: 10.1088/2631-6331/ab0c7e.
[18]	DENG B L, MO C Y, TOURNAT V, et al. Focusing and mode separation of elastic vector solitons in a 2D soft mechanical metamaterial [J]. Physical Review Letters, 2019, 123(2): 024101. DOI: 10.1103/physrevlett.123.024101.
[19]	HERBOLD E B, NESTERENKO V F. Propagation of rarefaction pulses in discrete materials with strain-softening behavior [J]. Physical Review Letters, 2013, 110(14): 144101. DOI: 10.1103/physrevlett.110.144101.
[20]	WANG L L. Foundations of stress waves [M]. New York: Elsevier, 2007.
[21]	CHREE C. The equations of an isotropic elastic solid in polar and cylindrical co-ordinates their solution and application [J]. Transactions of the Cambridge Philosophical Society, 1889, 14: 250.
[22]	LOVE A E H. A treatise on the mathematical theory of elasticity [M]. Cambridge: Cambridge University Press, 2013.
[23]	BRIZARD D, JACQUELIN E, RONEL S. Polynomial mode approximation for longitudinal wave dispersion in circular rods [J]. Journal of Sound and Vibration, 2019, 439: 388–397. DOI: 10.1016/j.jsv.2018.09.062.
[24]	DAVIES R M. A critical study of the Hopkinson pressure bar [J]. Philosophical Transactions of the Royal Society A: Mathematical Physical Sciences, 1948, 240(821): 375–457. DOI: 10.1098/rsta.1948.0001.
[25]	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 [J]. 力学学报, 2019, 51(6): 1820–1829. DOI: 10.6052/0459-1879-19-183. YANG H S, LI Y L, ZHOU F H. The propagation process and the geometric dispersion of a trapezoidal stress pulse in an elastic rod [J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(6): 1820–1829. DOI: 10.6052/0459-1879-19-183.
[26]	NAITOH M, DAIMARUYA M. The influence of a rise time of longitudinal impact on the propagation of elastic waves in a bar [J]. Bulletin of JSME, 1985, 28(235): 20–25. DOI: 10.1299/jsme1958.28.20.