中文摘要：

基于增量热场理论,引入悬索在温度变化下的热应力平衡状态,推导考虑温度效应的悬索非线性自由运动微分方程,并对其进行Galerkin离散以及线性分析。利用Lindstedt-Poincare法求解悬索非线性自由振动的近似解,通过算例研究温度变化对悬索非线性自由振动特性的影响。研究结果表明：温度变化不会改变悬索非线性运动方程形式,但是会影响非线性运动微分方程的线性及非线性项系数大小;对于垂度较小的悬索,温度上升,硬弹簧程度增强,反之则降低;而对于垂度较大的悬索,温度变化会导致悬索非线性自由振动时的软硬弹簧特性发生定量甚至定性的变化;升高和降低相同温度对悬索振动特性的影响呈现出明显不对称性。

英文摘要：

Based on the incremental thermal field theory, the thermal stress state of the suspended cable is introduced in this paper, and then the nonlinear free vibration differential equations under temperature changes are derived. The Galerkin method is employed to discretize these equations and the linear analysis is conducted. The Lindstedt-Poincare method is adopted to obtain the approximate solutions of the nonlinear free vibration. The research on the temperature effects on the nonlinear free vibration of suspended cables is conducted by some numerical calculations. Numerical results show that the nonlinear free vibration equations of motion do not change with the temperature changing, but the coefficients of the linear, quadratic and cubic nonlinearity terms change with the temperature effects. As to the suspended cable with small sag-to-span ratio, with the increase of the temperature, the hard spring characteristic increases too. However, the suspended cable with large sag-to-span ratio, the temperature changes will alter the soft-hard spring characteristics of the nonlinear free vibration quantitatively, even qualitatively. The effects of the same degrees of warming and cooling on the free vibration properties of suspended cables are obviously not symmetric.