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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。
Based on the incremental thermal field theory, the thermal stress equilibrium of the suspension cable under temperature change is introduced and the nonlinear free-motion differential equation of the suspension cable considering the temperature effect is deduced. The Galerkin discretization and linear analysis are carried out. The Lindstedt-Poincare method is used to solve the approximate solution of the nonlinear free vibration of the suspension cable. An example is given to study the influence of temperature variation on the nonlinear free vibration of the suspension cable. The results show that the change of temperature does not change the form of nonlinear equations of motion of the suspension cable, but it will affect the linear and nonlinear coefficient coefficients of nonlinear differential equations. For the small dip cables, the temperature rises and the hardness of the hard spring increases , And vice versa. On the other hand, the change of temperature leads to the quantitative or even qualitative change of the soft and hard spring characteristics when the cable is subjected to a nonlinear free vibration. The increase and decrease of the same temperature on the vibration characteristics of the suspension cable The impact showed obvious asymmetry.