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梯形应力脉冲在弹性杆中的传播过程和几何弥散

杨洪升 李玉龙 周风华

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
引用本文: 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 Hongsheng, Li Yulong, Zhou Fenghua. 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
Citation: Yang Hongsheng, Li Yulong, Zhou Fenghua. 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

梯形应力脉冲在弹性杆中的传播过程和几何弥散

doi: 10.6052/0459-1879-19-183
基金项目: 1) 国家自然科学基金资助项目(11390361);1) 国家自然科学基金资助项目(11932018)
详细信息
    通讯作者:

    周风华

  • 中图分类号: O347.4 +1

THE PROPAGATION PROCESS AND THE GEOMETRIC DISPERSION OF A TRAPEZOIDAL STRESS PULSE IN AN ELASTIC ROD

  • 摘要: 在应力波传播过程中,几何弥散效应往往难以避免.对应力波在弹性杆中传播的几何弥散效应进行解析分析,对于基础波动问题研究以及材料动态力学行为表征等课题,显得至关重要.本文简单说明了弹性杆中考虑横向惯性修正的一维 Rayleigh-Love应力波理论,概述了其波动控制方程的变分法推导过程;针对 Hopkinson杆实验中常用的梯形应力加载脉冲,建立了相应的偏微分方程初边值问题的求解模型,并运用 Laplace变换方法研究了脉冲在杆中传播的几何弥散现象;根据留数定理进行 Laplace反变换,给出了杆中不同位置和时刻的应力波的级数形式解析解,分析了计算项数对结果收敛性的影响;将解析计算结果与采用三维有限元数值模拟的计算结果进行对比,两者吻合程度良好,从而证明 Rayleigh-Love横向惯性修正理论可以有效地表征典型 Hopkinson杆实验中的几何弥散效应.在此基础上围绕梯形加载脉冲的弥散效应进行参数研究,定量描述了传播距离、泊松比、脉冲斜率等参数的影响.本文给出的 Rayleigh-Love杆在梯形加载条件下的解析解,揭示了几何弥散效应的本质规律,可以用于实际实验的弥散修正过程.

     

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出版历程
  • 收稿日期:  2019-07-15
  • 刊出日期:  2019-11-18

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