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欧拉-伯努利梁运动场的正交性及其能量传导特性分析

周俊 饶柱石 塔娜

周俊, 饶柱石, 塔娜. 欧拉-伯努利梁运动场的正交性及其能量传导特性分析[J]. 力学学报, 2015, 47(1): 135-146. doi: 10.6052/0459-1879-14-116
引用本文: 周俊, 饶柱石, 塔娜. 欧拉-伯努利梁运动场的正交性及其能量传导特性分析[J]. 力学学报, 2015, 47(1): 135-146. doi: 10.6052/0459-1879-14-116
Zhou Jun, Rao Zhushiy, Ta Na. THE ORTHOGONALITY AND ENERGY TRANSMITION CHARACTERISTICS OF EULER-BERNOULLI BEAM DYNAMIC MOTION FIELD[J]. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(1): 135-146. doi: 10.6052/0459-1879-14-116
Citation: Zhou Jun, Rao Zhushiy, Ta Na. THE ORTHOGONALITY AND ENERGY TRANSMITION CHARACTERISTICS OF EULER-BERNOULLI BEAM DYNAMIC MOTION FIELD[J]. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(1): 135-146. doi: 10.6052/0459-1879-14-116

欧拉-伯努利梁运动场的正交性及其能量传导特性分析

doi: 10.6052/0459-1879-14-116
基金项目: 国家重点基础研究发展计划资助项目(2014CB046302).
详细信息
    作者简介:

    饶柱石, 教授, 主要研究方向: 结构振动噪声分析与控制、生物力学、转子动力学.E-mail: tyuanhong@jnu.edu.cn

  • 中图分类号: O32.7

THE ORTHOGONALITY AND ENERGY TRANSMITION CHARACTERISTICS OF EULER-BERNOULLI BEAM DYNAMIC MOTION FIELD

Funds: The project was supported by the National Basic Research Program of China (2014CB046302).
  • 摘要: 从无阻尼欧拉—伯努利梁振动方程解析解出发, 推导了有限长梁的关于谱系数的时间—空间平均能量和功率流表达式. 在此基础上, 从泛函分析观点, 探讨了弯曲运动场: 衰减振动、行波模式分解关于能量、功率泛函的正交性. 结果表明: 弯曲衰减振动模式和行波模式关于功率流、机械能时间—空间平均是相互独立的, 即关于场能和场功率互不干涉, 满足叠加原理; 衰减振动场导能与行波场导能的重要区别在于功率流关于右、左衰振动模式分解不满足叠加原理, 即弯曲衰减振动场间的相互"干涉"是使其具有能量传导能力的内在原因. 通过右端集中阻尼器支撑的梁的稳态功率流仿真分析计算, 表明低频区振动导能不可忽略, 同时, 衰减振动场和行波场间存在一定的能量交换现象, 但随着频率升高, 振动场传导能量不断下降, 同时能量传导效率也不断下降.

     

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出版历程
  • 收稿日期:  2014-04-25
  • 修回日期:  2014-07-18
  • 刊出日期:  2015-01-18

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