中部与端部组合激励下悬索的主共振响应  

Primary Resonances of Suspended Cables under Simultaneously Mid-span and End Excitations

作　　者：余森涛 孙测世[1] 易鸣 Yu Sentao;Sun Ceshi;Yi Ming(College of Civil Engineering,Chongqing Jiaotong University,Chongqing 400074,China)

机构地区：[1]重庆交通大学土木工程学院,重庆400074

出　　处：《动力学与控制学报》2025年第1期33-40,共8页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(52378284);国家级大学生创新创业训练项目(202310618013)。

摘　　要：索结构具有质量小、刚度小、阻尼小的特点,容易在各种激励下发生横向振动,影响结构的安全、使用性能与寿命.为研究中部激励和端部激励的组合形式对悬索主共振响应的影响,考虑几何非线性,得到悬索无量纲微分控制方程,采用Galerkin法得到离散的常微分方程,再使用多尺度法对该方程进行求解.研究了不同中部和端部激励幅值比、不同中部和端部激励相位差以及不同中部激励位置对悬索主共振响应的影响.发现这些参数均不会改变主共振频响曲线的软硬状态,但激励幅值比和相位差会使曲线的各肢发生平移,或激励的相位差越接近π,悬索主共振响应越弱.中部激励位置的变化能使相频曲线同时发生平移和旋转,且其离端部激励越近,系统响应就越大.Cable structures,characterized by their low mass,low stiffness,and low damping,are prone to lateral vibrations under various excitations,which can significantly affect the safety,usability,and lifespan of the structure.To investigate the combined effects of mid-span and end excitations on the primary resonance of suspended cables,the dimensionless differential governing equations are derived,and the geometric nonlinearity is considered.The Galerkin method is employed to obtain discrete ordinary differential equations,which are then solved using the multiple scales method.The study explores the influence of different ratios of mid-span to end excitation amplitudes,different phase differences between mid-span and end excitations,and different positions of mid-span excitations on the primary resonance of suspended cables.It is found that these parameters do not alter the characteristic of the primary response-frequency curves.However,the amplitude ratio and phase difference result in shifts in the branches of the curves,and the smaller the amplitude or the closer the phase difference toπ,the weaker the primary resonance of the cable.Changes in the position of mid-span excitation cause simultaneous translation and rotation of the phase-frequency curve,and the closer it is to the end excitation,the larger the system response.

关 键 词：悬索 非线性振动 中部激励 端部激励 主共振 

分 类 号：O322[理学—一般力学与力学基础] U448.27[理学—力学]