考虑温度效应的索梁面内动力学建模及特性分析

根据增量热场理论，温度变化影响下索梁结构会形成新的热应力平衡状态．因此基于已有的索梁结构非线性动力学模型，结合与斜拉索张拉力和垂度相关的无量纲参数，重新建立考虑温度变化影响下索梁结构面内振动的动力学模型，并推导其面内非线性运动方程．接着开展特征值分析，得到包含温度效应的索梁结构面内振动频率的超越方程及模态振型函数．通过算例研究温度变化对不同刚度比的索梁结构影响，得到其前四阶面内振动的模态频率与温度变化的关系曲线．研究结果表明：面内模态频率受温度变化影响明显，其影响程度与刚度比大小和模态的阶数密切相关，温度变化对低阶模态频率的影响比对高阶模态频率影响更为复杂；升温和降温对索梁结构面内振动特性的影响不对称；此外温度变化会导致频率偏转点的位置发生漂移．

In-Plane Vibration Modeling and Characteristic Analysis of Cable-Stayed Beam Considering Temperature Effects

Based on the incremental thermal field theory, the new thermal stressed configuration of the cable stayed beam is investigated. Based on the existing nonlinear dynamic model of the cable stayed beam, this paper establishes the thermo-elasticity analytical model of the cable stayed beam by introducing two non-dimansional parameters for the cable tension force and the sag, and derives the corresponding in-plane vibration equations of motion. Eigenvalue analysis is performed to obtain the natural frequencies and mode shapes of the cable stayed beam with temperature effects, and two types of eignevalue solutions are obtained. The temperature effects on the first four in-plane mode frequencies of the cable stayed beam with different stiffness ratios are investigated. Numerical results show that the temperature effects on the mode frequencies are obvious, and it is close related with the stiffness ratio and the order of the mode. The warming and cooling effects on the vibration characteristics of the cable stayed beam are asymmetric. The veering points between two different mode frequencies are found to be drifted when the temperature changes.