温度和桥面激励联合作用下斜拉索非线性振动特性分析

研究热状态下受桥面激励作用的超长斜拉索主参数共振问题。计入斜拉索初始垂度和几何非线性的影响,建立温度场中斜拉索的非线性振动力学模型,推导出热状态下受桥面激励作用的斜拉索面内参数振动控制方程,利用多尺度法求解系统主参数共振的近似理论解,并编制程序进行数值计算,分析温度变化、激励幅值、调谐值、索力、阻尼比对系统振动的影响。结果表明:随着温度升高,斜拉索主参数共振区增大,但其振幅有减小趋势;增大桥面激励幅值,会使得拉索参数共振区显著增大,而增大索力和阻尼,拉索共振区将减小;拉索发生参数振动时具有硬弹簧特性,幅频曲线随调谐值的增大存在多值响应,会出现"跳跃现象"。

Vibration Analysis of Long Cables Subjected to Deck Excitation and TemperatureWANG Feng , WEN Xiao-xu , Chen Fu-qing

The main parametric vibration is studied for long cables subjected to deck excitation in temperature field. Considering cable sag and geometrical nonlinearity, the nonlinear vibration equation of long cables in temperature field is established. According to multiple scales method for nonlinear vibration analysis, the approximation of parametric resonance of the system is solved. Numerical analysis of the influence of temperature, excitation, detuning, cable force, damping is carried out. The results shows that the primary parametric resonance zone of cables increase with the increase of temperature, but its amplitude decrease; When excitation increasing, the resonance zone and amplitude increase, but the vibration zone will be decreased with cable force increasing; The greater the cable damping is, the resonance area is smaller. The cables have a kind hard spring property. Due to its nonlinearity the amplitude frequency response has multivalent response, which is "jump phenomenon".