Abstract: In order to solve dynamic responses of continuous beams with variable cross-section more efficiently, taking a common kind of continuous beams with variable cross-section as the breakthrough point, the segmental transfer matrix deduction method of continuous beams with variable cross-section and vibration characteristics analysis method were established based on transfer matrix method; meanwhile, the calculation method of dynamic time history under the action of mobile spring quality was also researched. Firstly, starting from the variable cross-section beam bending vibration differential equation, the segmental element transfer matrix deduction method was established; and then the transfer matrix construction method of continuous beams with variable cross-section was derived and its self vibration characteristics analysis was also completed. Secondly, the calculation of dynamic time history of continuous beams with variable cross-section under the excitation of mobile spring quality was completed, combining with Newmark-β method. Finally, the numerical simulation program of dynamic analysis available for continuous beams with variable cross-section was developed in MATLAB. The calculation results show that the proposed method is not only correct and reliable, but also more simple and efficient than the finite element method, which has a certain application prospect.

Key words: bridge engineering, transfer matrix method, continuous beams with variable cross-section, self-vibration characteristics analysis, dynamic time-history analysis

摘要： 从建立更为快捷的变截面连续梁动力分析方法出发，以某一类常见结构形式的变截面梁为切入点，基于传递矩阵法建立了变截面连续梁的节段式传递矩阵推导方法、自振特性分析方法，研究了移动弹簧质量作用下的动力时程计算方法。首先，由变截面梁横向弯曲振动微分方程出发，建立节段式单元传递矩阵的推导方法；然后，建立变截面连续梁整体传递矩阵的构建方法，完成其自振特性分析；之后，结合Newmark-β法完成移动弹簧质量激励下变截面连续梁的动力时程计算；最后，以MATLAB为平台开发了适用于变截面连续梁动力分析的数值仿真模拟程序。计算结果表明：该变截面梁动力分析方法不仅正确可靠，相比于有限元法还更为简单、高效，具有一定的应用前景。

关键词: 桥梁工程, 传递矩阵法, 变截面连续梁, 自振特性分析, 动力时程分析