移动荷载下梁索组合结构瞬态响应分析

为验证波动理论在求解梁索组合结构自振特性和冲击响应问题中的适用性，初步探讨移动荷载下弹性波在结构中的传递特征，从铁木辛柯梁的横向振动微分方程和拉索的纵向波动方程出发，推导了移动荷载作用下梁索组合结构的动力学响应函数，通过构造回传路径矩阵，得到结构响应的波动解。为解决传统回传路径矩阵法（MRRM）在计算弯曲波传递过程中回传路径矩阵求逆困难的问题，基于离散傅里叶变换思想(DFT)，推导出结构瞬态响应的级数解，用试验和有限元数值算例对改进后的MRRM法进行验证。结果发现，在30km/h的车速下，本文算法计算得到的跨中最大动应变和有限元结果偏差为5%，与试验结果相比偏差8%；40km/h的车速下，理论最大值与有限元偏差为4%，与试验结果相比偏差9.8%。最后，以梁索组合结构为研究对象，本文算法计算得到的结构前五阶自振频率与有限元结果最大偏差为0.29%，前二阶自振频率偏差为0%。进一步分析移动荷载下，梁索组合结构的波动响应特点，将理论结果与有限元数值结果进行比对，结果具有较高的吻合度。可推知，本文算法在计算移动荷载下桥梁结构的瞬态波动响应方面具有较高的可靠性。通过结构频谱分析，发现移动荷载下，铁木辛柯梁中弯曲波主要为频率分量低于结构2倍自振频率的低频响应。进而在改进后的MRRM基础上，探索基于结构自振特性的频域合理选取准则，进一步提高MRRM法求解波动响应的计算效率。

Transient Response Analysis of Cable–beam Structural System Under Moving Load

To verify the applicability of wave theory in studying the free vibration characteristics and impact response of cable-beam structure, and to preliminarily explore the behaviors of elastic wave propagation through the structure under moving load, the dynamic response function was derived from the transverse vibration differential equation of Timoshenko beam and the longitudinal wave equation of cables. The reverberation-ray matrix was used to obtain the wave form solution of the structural response. Based on the idea of discrete Fourier transform (DFT), the series solution of structural transient response was derived to solve the inverse problem of traditional reverberation-ray matrix (MRRM). The improved MRRM was verified by experiment and finite element method(FEM). The results shown that at the speed of 30 km /h, the deviation between the theoretical maximum strain and FEM results was 5%, and that between theoretical and experimental results was 8%. When the vehicle speed was 40km/h, the deviation between the theoretical maximum strain and FEM results was 4%, which was 9.8% between theoretical and experimental results. Taking the beam-cable system as the research object, the maximum deviation between the first five natural frequencies calculated by improved MRRM and FEM was 0.29%, and the deviation between the first two natural frequencies was 0%. The wave response characteristics of the cable-stayed beam under moving load are analyzed and the theoretical results were in good agreement with the FEM results. It could be inferred that the improved MRRM had high reliability in calculating the transient wave response of bridge structure under moving load. Based on the analysis of the frequency domain response, it was found that the flexural waves in Timoshenko beam under moving load were mainly low frequency responses whose frequencies were lower than 2 times of the fundamental frequency of the structure. Furthermore, the reasonable selection criteria of frequency range was explored in the process of finding the wave response, so as to further improve the calculation efficiency of MRRM.