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Temperature effects on the resonance responses of stay cables under support excitation[J].计算力学学报,2017,(5):644~649

Temperature effects on the resonance responses of stay cables under support excitation
Temperature effects on the resonance responses of stay cables under support excitation

DOI：10.7511/jslx201705017

 作者 单位 E-mail 赵珧冰 华侨大学 土木工程学院, 厦门 361021;湖南大学 土木工程学院, 长沙 410082 Ybzhao@hqu.edu.cn 孙测世 重庆交通大学 土木工程学院, 重庆 400074;湖南大学 土木工程学院, 长沙 410082

基于增量热场理论，利用Hamilton变分原理，通过引入与张拉力和垂度相关的无量纲参数，建立了考虑温度变化影响下斜拉索非线性动力学模型，并推导其面内/外非线性运动微分方程。考虑斜拉索受端部激励，利用Galerkin法得到离散后的无穷维常微分方程组。面内和面外运动各取前两阶模态，向前和向后扫频，利用龙格-库塔法数值积分求解常微分方程组，得到共振区域的幅频响应曲线。算例分析表明，温度变化和斜拉索固有频率呈反比例关系；温度变化会导致斜拉索共振特性发生定性和定量的改变，如共振区间发生漂移、跳跃点位置发生移动、共振响应幅值发生改变；端部位移激励下，温度变化有可能导致斜拉索更多模态受到激发，从而影响各阶模态的能量以及模态间的能量传递。

Based on the incremental thermal field theory,the nonlinear dynamic model of stay cables with thermal effects was established by introducing two non-dimensional parameters in the cable tension force and the sag,and the nonlinear vibration equations of motion were derived by the Hamilton' s principle.Under support excitation,these differential equations were discretized by the Galerkin method. The first two in-plane and out-of-plane mode shapes were selected in forming the dynamic response and the Runge-Kutta method was used to solve these ordinary differential equations from forward sweeping to backward sweeping.The amplitude-frequency response curves of the numerical examples show that the natural frequencies decrease with temperature changes; the resonance interval drifts;the location of the jump point shifts; the resonance response amplitudes change;under the excitation of the support motions,many more modes might be excited when the temperature is changed,so the energy of different modes and the energy transfer between different modes varies under temperature changes.