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 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.
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.

• 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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