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铁木辛柯梁中的卸载弯曲波及二次断裂

龙龙 郑宇轩 周风华 任会兰 宁建国

龙龙, 郑宇轩, 周风华, 任会兰, 宁建国. 铁木辛柯梁中的卸载弯曲波及二次断裂[J]. 力学学报, 2021, 53(6): 1658-1670. doi: 10.6052/0459-1879-21-106
引用本文: 龙龙, 郑宇轩, 周风华, 任会兰, 宁建国. 铁木辛柯梁中的卸载弯曲波及二次断裂[J]. 力学学报, 2021, 53(6): 1658-1670. doi: 10.6052/0459-1879-21-106
Long Long, Zheng Yuxuan, Zhou Fenghua, Ren Huilan, Ning Jianguo. UNLOADING FLEXURAL STRESS WAVE IN A TIMOSHENKO BEAM AND THE SECONDARY FRACTURE OF THE BEAM[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(6): 1658-1670. doi: 10.6052/0459-1879-21-106
Citation: Long Long, Zheng Yuxuan, Zhou Fenghua, Ren Huilan, Ning Jianguo. UNLOADING FLEXURAL STRESS WAVE IN A TIMOSHENKO BEAM AND THE SECONDARY FRACTURE OF THE BEAM[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(6): 1658-1670. doi: 10.6052/0459-1879-21-106

铁木辛柯梁中的卸载弯曲波及二次断裂

doi: 10.6052/0459-1879-21-106
基金项目: 1)国家自然科学基金资助项目(11390361);国家自然科学基金资助项目(12072169)
详细信息
    作者简介:

    2)周风华, 研究员, 主要研究方向: 冲击动力学. E-mail: zhoufenghua@nbu.edu.cn

    通讯作者:

    周风华

  • 中图分类号: O347.4+1

UNLOADING FLEXURAL STRESS WAVE IN A TIMOSHENKO BEAM AND THE SECONDARY FRACTURE OF THE BEAM

  • 摘要: 半无限长梁承受恒定弯矩作用后, 如果自由端的初始弯矩突然释放, 将在梁中激发出一列卸载弯曲应力波. 采用铁木辛柯梁和瑞利梁来研究突然卸载所激发出的弯曲波的传播特征. 利用拉普拉斯变换方法进行分析, 首先推导出铁木辛柯梁和瑞利梁中的卸载弯曲波的像函数解析解, 采用数值反变换方法给出了时域上波传播的响应解, 并研究了梁中各点的横向位移、弯矩和剪力随时间的变化规律. 计算结果表明: 与简化的欧拉梁不同, 旋转惯性的引入使铁木辛柯梁和瑞利梁中的弯曲波传播具有强烈的局部化效应, 特别是梁中各点经历的弯矩变化, 和其距离自由端的位置相关, 不同时刻的弯矩峰值大小不同;瑞利梁中离自由端不同距离各点的峰值弯矩先增大后降低, 最后达到一个渐近值;铁木辛柯梁中各点的峰值弯矩总体上随着时间单调增大到同一个渐近值, 该渐近值与欧拉梁中的峰值弯矩值相同, 均为1.43.切应力效应的引入进一步降低了铁木辛柯梁中卸载弯曲波的波速, 同时也使得铁木辛柯梁中弯矩峰值的最大值小于瑞利梁中的最大值. 对于脆性细长梁的纯弯曲断裂, 铁木辛柯梁可以较好地预测二次断裂的发生位置, 相应的碎片尺寸约为7倍梁横截面厚度.

     

  • [1] Miklowitz J. Elastic waves created during tensile fracture--The phenomenon of a second fracture. Journal Applied Mechanics, 1953, 3: 122-130
    [2] Phillips JW. Stress pulses produced during the fracture of brittle tensile specimens. International Journal of Solids and Structures, 1970, 6: 1403-1412
    [3] Kolsky H. The stress pulses propagated as a result of the rapid growth of brittle fracture. Engineering Fracture Mechanics, 1973, 5: 513-522
    [4] Kinra V. Stress pulses emitted during fracture in tension. International Journal of Solids and Structures, 1976, 12, 803-808
    [5] Bodner SR. Stress waves due to fracture of glass in bending. Journal of the Mechanics and Physics of Solids, 1973, 21: 1-6
    [6] Kinra V, Kolsky H. The interaction between bending fractures and the emitted stress waves. Engineering Fracture Mechanics, 1977, 9: 423432
    [7] Schindler HJ, Kolsky H. Multiple fractures produced by the bending of brittle beams. Journal of the Mechanics and Physics of Solids, 1983, 31: 427-436
    [8] Audoly B, Neukirch S. Fragmentation of rods by cascading cracks: Why spaghetti does not break in half. Physical Review Letters, 2005, 95: 095505
    [9] Heisser RH, Patil VP, Stoop N, et al. Controlling fracture cascades through twisting and quenching. Proceedings of the National Academy of Sciences of the United States of America, 2018, 115: 65-70
    [10] Long L, Zheng Y, Zhou F, et al. Towards further understanding the secondary fracture during spaghetti bent break. Materials, 2021, 14: 189
    [11] 王礼立. 应力波基础. 北京: 国防工业出版社, 2005

    (Wang Lili. Foundation of Stress Wave. Beijing: National Defence Industry Press, 2005 (in Chinese))
    [12] Rayleigh L. The Theory of Sound. Dover: New York, 1945: 1877-1878
    [13] Timoshenko SP. On the correction factor for shear of the differential equation for transverse vibrations of bars of uniform cross-section. Philosophical Magazine, 1921: 744
    [14] Graff KF. Wave Motions in Solids. New York: Dover Publications, Inc, 1975: 186
    [15] Timoshenko SP. Schwingungsprobleme der Technik. Julius Springer, 1932
    [16] Mindlin RD, Deresiewicz H. Timoshenko's shear coefficient for flexural vibrations of beams. Technical Report No. 10, ONR Project NR064-388, 1953, Department of Civil Engineering, New York: Columbia University
    [17] Cowper GR. The shear coefficient in Timoshenko's beam theory. Journal Applied Mechanics, 1966, 33(2): 335-340
    [18] Stephen NG. Timoshenko's shear coefficient from a beam subjected to gravity loading. Journal of Applied Mechanics, 1980, 47(1): 121-127
    [19] Hutchinson JR. Transverse vibration of beams, exact versus approximate solutions. Journal of Applied Mechanics, 1981, 48(12): 923-928
    [20] Timoshenko S, James MG. Mechanics of Materials. Van Nostrand Reinhold Co., 1972: 207
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出版历程
  • 收稿日期:  2021-03-17
  • 刊出日期:  2021-06-01

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