含轴力高频振动梁的能量辐射传递模型

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摘要为考察轴力对梁高频振动的影响，建立了轴力作用下梁的能量辐射传递模型。针对具有恒定轴力作用的Euler-Bernoulli梁，引入受轴力影响的波数和群速度，建立了能量密度控制方程，推导了轴力作用下梁的能量密度和能量强度的核函数。实源强度由导纳法计算得到的输入功率表示，虚源强度通过边界的能量平衡方程确定，根据惠更斯原理，梁的能量响应由实源产生的直接场与虚源产生的反射场线性叠加得到。最后，通过将能量辐射传递法(RETM)获得的结果与波传播法解析解进行比较，分析了轴力作用下无限结构导纳的适用性，验证了本文所提RETM的正确性，同时分析了轴力对梁能量响应的影响。

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	王硕
	黄进安
	代成浩
	陈海波

关键词 ：能量辐射传递模型, 轴力, 欧拉梁, 高频振动, 能量响应

Abstract：In order to investigate the influence of axial force on the high frequency vibration of beam, the energy radiation transfer model of beam under axial force is established. For the Euler-Bernoulli beam with constant axial force, the wave number and group velocity affected by the axial force are introduced, the governing equation of energy density is established, and the kernel functions of energy density and energy intensity of the beam under axial force are derived. The real source strength is expressed by the input power calculated by the admittance method, and the virtual source strengths are determined by the energy balance equations at the boundaries. According to Huygens principle, the energy response of beam is obtained by the linear superposition of the direct field generated by the real source and the reflected field generated by the virtual sources. Finally, by comparing the results obtained by the energy radiation transfer method (RETM) with the analytical solution calculated by the wave propagation method, the applicability of the input admittance of infinite structure under the action of axial force is analyzed, the accuracy of the proposed RETM is verified, and the influence of axial force on the energy response of beam is also analyzed.

Key words： Energy radiative transfer model Axial force Euler beam High frequency vibration Energy response

收稿日期: 2022-01-24 出版日期: 2023-04-28

引用本文:

王硕，黄进安，代成浩，陈海波. 含轴力高频振动梁的能量辐射传递模型[J]. 振动与冲击, 2023, 42(8): 134-141.
WANG Shuo，HUANG Jin’an，DAI Chenghao，CHEN Haibo. A radiative energy transfer model for a high-frequency vibrating beam under axial force. JOURNAL OF VIBRATION AND SHOCK, 2023, 42(8): 134-141.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2023/V42/I8/134

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