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

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