CFRP斜拉索模态耦合内共振特性

Property of Mode-coupled Internal-resonance of CFRP Cables

为研究CFRP拉索模态耦合内共振特性,建立了反映拉索面内、外1阶模态耦合作用的二自由度振动模型,该模型考虑了索的垂度、大位移等引起的几何非线性。利用该模型,采用数值方法分析了相同条件下的CFRP拉索和钢拉索在纯平面和非平面荷载作用下的内共振响应,并研究了外激励幅值、阻尼比、初始扰动等对内共振的影响。研究结果表明,当拉索的面内、外频率满足共振条件时,拉索同时发生荷载作用面内的主共振和面内、外的内共振;随着外激励幅值的增大,2种拉索面内、外最大位移增大,当外激励幅值小于一定值时,2种拉索不能发生内共振;随着阻尼比的增大,拉索发生内共振时的最大和稳态振幅呈现减小的趋势,当阻尼比分别增大到一定程度时,2种拉索不能发生内共振;随着初始扰动的增大,拉索的面内、外最大振幅和稳态振幅基本保持不变,但能量从面内传递到面外所用的时间变短;在运动过程中,CFRP索拍频明显高于钢索,其由瞬态振动进入到稳态运动的时间均早于钢索,而最大振幅和稳态振幅小于钢索。

In order to investigate the mode-coupled internal-resonance characteristics of CFRP cables,a two-degree-of-freedom vibration model was established to reflect the first-order mode coupling of the cable in plane and out of plane.The geometrical nonlinearity caused by sag and large displacement of cables was taken into consideration.On the basis of the model,the internal resonance responses of CFRP cables and steel cables with the same conditions under pure plane and non-plane loads were analyzed by the numerical method.The effects of external excitation amplitude,damping ratio and initial disturbance on internal-resonance characteristics were investigated.The results show that when the frequencies of cables in plane and out of plane satisfy the resonance condition,the primary resonance in plane occurs along with the internal resonance in plane and out of plane.With the increase of the external excitation amplitude,the maximum displacements in plane and out of plane increase. When the external excitation amplitude is less than a certain value,the internal resonance is not likely to occur.With the increasing damping ratio,the maximum and steady-state amplitudes of cables tend to decline.When the damping ratios increase to a certain value,the internal resonance is not likely to occur.With the increase of the initial disturbance,the maximum amplitude and steady-state amplitudes of the cable almost remain unchanged but it is shorter for energy transferring from the in-plane to the out-of-plane.During the course of motion,the beat frequency of CFRP cable is significantly higher than that of the steel cable.It is more quickly for the CFRP cable from transient vibration to steady motion.In particular,the maximum amplitude and steady amplitude of CFRP cable are much smaller than those of the steel cable.