考虑温度效应的索梁结构非线性动力学建模及振动特性研究

The cable stayed beam which is widely used in engineering is easily affected by the variety of environment temperature, and the state of serviceability would be affected because its mechanical characteristic would be changed obviously by the temperature changes. Hence, the vibration characteristics of the cable stayed beam with thermal effects become a key problem to be solved. The previous studies show that the nonlinear vibration characteristics of the cable and beam would be changed by the temperature effects qualitatively and quantitatively. Hereby, based on the cable stayed beam under thermal effects, the nonlinear dynamics model and high dimensional nonlinear differential equations of motion will be derived and these approximate analyses, numerical calculations and experimental investigations will be performed via the incremental thermal field theory, thermal stress theory, nonlinear dynamics theory and modern testing techniques. The project is expected to reveal the linear and nonlinear vibration characteristics of the cable stayed beam under the uniform and gradient temperature fields, and the temperature effects on the internal resonance of the system based on the energy transmission principle will be investigated. The experiment on the cable stayed beam will be done to validate the approximate analyses and numerical results and also modify the obtained theoretical model. This project is of great significance and application prospect not only to enrich the nonlinear vibration theoretical and experiment investigations of the cable stayed beam, but also lay the theoretical foundation and provide technical reserves for the temperature effects in the designing, construction, health monitoring and condition assessment of the cable stayed beam.

工程中广泛应用的索梁结构极易受到环境温度变化影响，导致力学特性发生明显改变，影响正常使用，因此温度变化对索梁结构振动特性影响机理成为亟待解决的关键问题。前期研究表明温度变化会定性或定量地改变拉索和梁的非线性振动特性。据此，本项目将综合运用增量热场理论、热应力理论、非线性动力学理论和现代测试技术，以考虑温度效应的索梁结构为研究对象，建立和推导其非线性动力学模型和高维运动微分方程，并开展近似分析、数值计算和实验研究。项目将揭示均匀温度和梯度温度变化对索梁结构的线性和非线性振动特性的影响机理；基于能量传输原理，阐述温度变化对系统内共振响应的影响；通过模型实验，验证部分近似分析和数值计算结果，修正力学模型。研究成果将进一步丰富索梁结构非线性动力学理论和实验研究，同时为索梁结构设计、施工、健康监测和状态评估中的温度效应研究奠定理论基础和提供技术储备，具有重要的科学意义及应用前景。

由柔性索和弹性梁组合而成的索梁结构，在工程中引用极其广泛，加之周围温度场变化剧烈，导致其索力、主梁应力、应变、横截面面积、材料弹性模量和阻尼系数等发生改变，使得系统的线性和非线性动力学特性变得更加复杂。本项目以均匀、整体变化温度场中的索（悬索和斜拉索）、梁和索梁结构为研究对象，基于增量热场理论、热应力理论、线性和非线性动力学理论以及实验测试技术，综合考虑温度效应、材料和几何非线性等因素，建立了考虑温度效应影响下的索、梁和索梁结构的非线性动力学模型，推导出高维非线性动力学方程。考虑支座位移激励，单谐波以及多频谐波激励作用，采用近似分析方法（多尺度法、谐波平衡法和Lindstedt-Poincare法等）和数值计算方法（龙格-库塔法、牛顿-拉夫逊法、打靶法和弧长延拓法）得到方程的近似解和数值解。利用幅频响应曲线、调谐相位曲线、激励响应幅值曲线、时程曲线、相位图、庞加莱截面以及频率谱等，探究了温度变化对已建立模型的非线性自由振动、主共振、次/超谐波、联合/组合共振以及内共振响应的影响，揭示了温度变化对系统振动特性的影响机理。此外，还开展了索梁结构的非线性动力学实验测试，探究了索和梁耦合振动时拉索的非线性频率以及空间耦合运动规律，揭示了非线性振动中“跳跃”现象的过程。本项目进一步丰富了索梁结构非线性动力学理论和实验研究，为索结构设计、施工、健康监测和状态评估中的温度效应奠定了理论基础。综上所示，本项目执行期内达到了预期研究目标，完成了既定研究内容。