含轴力高频振动梁的能量辐射传递模型  

A radiative energy transfer model for a high-frequency vibrating beam under axial force

作　　者：王硕[1] 黄进安 代成浩 陈海波[1] WANG Shuo;HUANG Jin’an;DAI Chenghao;CHEN Haibo(CAS Key Laboratory of Mechanical Behavior and Design of Materials,Department of Modern Mechanics,University of Science and Technology of China,Hefei 230027,China)

机构地区：[1]中国科学技术大学近代力学系、中国科学院材料力学行为与设计重点实验室,合肥230027

出　　处：《振动与冲击》2023年第8期134-141,共8页Journal of Vibration and Shock

基　　金：国家自然科学基金(11772322);中国科学院战略性先导科技专项(B类)子课题(XDB22040502)。

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,建立能量密度控制方程,推导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。通过将能量辐射传递法(energy radiative transfer model,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,验证所提RETM的正确性,同时分析了轴力对梁能量响应的影响。In order to investigate the influence of axial force on the high frequency vibration of a beam,a energy radiation transfer model of the beam under axial force was established.For the Euler-Bernoulli beam with constant axial force,the wave number and group velocity affected by the axial force were introduced,the governing equation of energy density was established,and the kernel functions of energy density and energy intensity of the beam under axial force were derived.The real source strength was expressed by the input power calculated by the admittance method,and the virtual source strengths were determined by the energy balance equations at the boundaries.According to the Huygens principle,the energy response of the beam was 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 the infinite structure under the action of axial force was analyzed,the accuracy of the proposed RETM was verified,and the influence of axial force on the energy response of beam was also analyzed.

关 键 词：能量辐射传递模型(RETM) 轴力 欧拉梁 高频振动 能量响应 

分 类 号：TB532[理学—物理]