考虑阻尼的无限长小垂度缆索弹性波的传播  

PROPAGATION OF ELASTIC WAVE IN INFINITE CABLE WITH SMALL SAG CONSIDERING DAMPING

作　　者：李丽君 曾晓辉[1,2] 崔哲华 吴晗 Li Lijun;Zeng Xiaohui;Cui Zhehua;Wu Han(Key Laboratory for Mechanics in Fluid Solid Coupling Systems,Institute of Mechanics,Chinese Academy of Sciences,Beijing 100190,China;School of Engineering Science,University of Chinese Academy of Sciences,Beijing 100049,China;School of Future Technology,University of Chinese Academy of Sciences,Beijing 100049,China)

机构地区：[1]中国科学院力学研究所流固耦合系统力学重点实验室,北京100190 [2]中国科学院大学工程科学学院,北京100049 [3]中国科学院大学未来技术学院,北京100049

出　　处：《力学学报》2023年第5期1138-1150,共13页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家重点研发计划(2022YFB4201500);国家自然科学基金(11672306)资助项目。

摘　　要：缆索结构被广泛应用于电气、土木、海洋和航空工程等领域,随着缆索在工程中的应用长度越来越长,高阶振动越来越明显,研究时应该考虑扰动沿着缆索的传播.现有对缆索弹性波传播的研究中,通常不考虑阻尼项,然而阻尼对于波的传播有着重要影响.文章考虑阻尼的影响,发展了包含阻尼项的三维弹性缆索运动方程.通过求解上述含阻尼项的运动方程,分别考察了面内面外弹性波的频率关系、相速度和群速度等自由传播特性,进而通过计算无限长弹性缆索在初始余弦型脉冲作用下的位移响应,分析扰动沿着该缆索的传播规律,考察波的色散现象以及阻尼对于缆索弹性波传播的影响.结果表明,考虑阻尼后,面内波和面外波均为色散波,面内波在曲率的作用下,为高度色散波.此外,在阻尼的影响下,波的峰值在传播过程不断减小,且波的后缘端点响应总是高于前缘端点响应.Cable structures are widely used in electrical,civil,marine and aviation engineering.As cable in engineering longer and longer,the high-order vibration becomes more and more obvious.Accordingly,the disturbance propagation should be considered in the study.In the existing research on the propagation of elastic waves in cables,the damping is usually not considered.However,damping has an important influence on the propagation of waves.We developed the motion equation of three-dimensional elastic cable by considering damping into equation.The free propagation characteristics of in-plane and out-of-plane waves are discussed respectively by solving the equations of motion above,including frequency relation,phase velocity,group velocity.And then,the wave propagation law of the cable is further discussed by calculating the displacement response under the initial cosine pulse.Besides,we study the wave dispersion and the influence of damping on the propagation of elastic waves in cables.The results show that both in-plane and outplane waves are dispersive while damping is considered.In addition,the in-plane waves are highly dispersive with the curvature considered.In addition,the crest of wave dissipates in wave propagation,and the response of trailing edge is higher than the leading edge while damping is considered.

关 键 词：缆索弹性波 波的色散 自由振动 阻尼 波的衰减 

分 类 号：O347.41[理学—固体力学]