斜拉桥塔一索一桥耦合连续模型及其内共振分析
张妍，王怀磊，杨杰
摘要:研究斜拉桥桥塔-斜拉索-桥面的连续耦合振动模型及其2:2:1和1:1:1内共振问题.计及拉索的重力垂度,倾角及空气阻尼等因素,将桥面简化为一端固支,一端受弹簧力作用的Bernoulli-Euler梁,桥塔视作受弹簧拉力和阻尼力的质量块,建立了桥塔一拉索一桥面连续耦合非线性振动模型.利用多尺度方法得到了系统发生内共振的条件,并求出系统的三个自由度稳态运动幅值所满足的关系式. 对系统的内共振进行了数值模拟,验证了理论分析的正确性.结果表明,桥塔和拉索在初始扰动下会发生1:1内共振,桥面在一次近似意义上仅仅提供了内共振产生的约束条件,但在内共振过程中没有参与系统各部分之间的能量交换.最后发现一定条件下,系统会出现混沌运动.
关键词：斜拉桥；桥塔；桥面；非线性振动；内共振
A continuous model of coupled cable-tower-decks and its resonance vibration
Yan Zhang, Huailei Wang, Jie Yang
Abstract：A nonlinear coupled vibration model of towers and cables and bridge decks and its 2:2:1 or 1:1:1re sonance is investigated with taking the initial sag, the angle of the cable and the air damping into consideration. The deck is simplified as a Bernoulli-Euler beam which fixed on one end and attached to the spring on the other end, the tower as a concentrated mass that subject to the spring and damp. A nonlinear vibration system of tower-cable-deck is established. With the application of the method of multiple scales, the condition of yielding the inner resonance and the formula of the amplitude of the steady -state vibration are obtained. The validity of the analysis is verified by the numerical simulation. The results show that the 2:2:1 and 1:1:1 intern al resonance will occur under some initial conditions in the cable and the deck, while the tower just provide a restriction on the occurrence of internal resonance but doesn't take part in the energy exchange of the syste m in the first order approximation. The phenomena of chaos are also found.
Keyword：cable-stayed bridge tower; deck; nonlinear vibration; internal resonance
原文链接：http://lib.cqvip.com/Qikan/Article/Detail?id=35137530
