竖向激励下斜拉桥的内共振动力响应分析

将斜拉桥简化为单自由度振子-索模型,对振动方程进行线性简化;采用Matlab程序和Ansys程序分别对简化模型进行模态分析。索桥频率比分别取0.98、1.00和1.04,在模型支座处施加竖向加速度激励,进行时程分析,求解了系统的动力响应。分析结果表明,单自由度振子-索模型分析斜拉桥的振动问题是有效的和可行的。当索桥频率比在1∶1附近时,拉索与振子的振动存在耦合效应,产生内共振;在简谐支座竖向加速度激励下,系统的动力响应存在瞬态阶段和稳态阶段,响应峰值出现在瞬态阶段,拉索振动以第1阶模态振型为主;拉索动索力和拉索与振子间的相互作用在稳态阶段的幅值均出现漂移现象,拉索动索力变化幅度剧烈。因此,在斜拉桥设计和索力测试中要考虑索桥内共振的影响。

Dynamic Response Analysis of Internal Resonance for Cable-stayed Bridges under Vertical Excitation

A cable-stayed bridge was simplified by a single-freedom-oscillator-cable model and the vibration equation was linearly simplified. Modal analysis was done with Matlab program and Ansys program respectively. Frequency ratio between a cable and the bridge is 0.98, 1.00 and 1.04. Vertical acceleration excitation was acted on the model at the supports. Time-history analysis was done to solve the system dynamic responses. Analysis results show that it is effective and feasible to solve the vibration problems of a cable-stayed bridge with a single-freedom-oscillator-cable model. When frequency ratio is close to 1:1, the cable vibration is coupled with the oscillator vibration and internal resonance occurs. The system dynamic responses are divided into a transient stage and a steady stage. The peak values appear at the transient stage. The cable vibration is characterized with the first vibration mode. Peak values of the dynamic tension force and the interanction between the cable and the oscillator drift from the center in steady stage. Dynamic tension forces change sharply. Therefore, considerations must be given on the internal resonance in cable-stayed bridges and cable force measuring.