柔性结构桥梁在非定常气动力作用下的近似周期解

The Periodic Solution of Flexible Structural Bridge under the Unsteady Aerodynamics

以Tacoma大桥为例,针对工程中一类柔性结构桥梁在非定常气动力作用下的非线性动力学模型,在对其奇点类型和其周期运动存在性进行定性分析的基础上,利用谐波平衡法进行了定量分析,得到了该系统稳态的近似周期解。最后,通过数值仿真对理论结果进行了验证。结果表明,当风速在某一个区域内时,所得到的解析结果和数值结果非常接近,且与定性分析的结论一致。此时,由于长时间的周期振动会造成结构疲劳破坏,甚至可能会严重影响桥梁结构的安全,本文的研究结果在振动工程计算和理论设计中具有一定的指导意义。

In this paper, a nonlinear dynamic model derived from engineering is investigated. The dynamic charac-teristic is analyzed by using the geometrical theory of ordinary differential equations. The Tacoma bridge is taken for example, the quantitative analysis of the nonlinear dynamical model of a flexible structural bridge under the un-steady aerodynamics from engineering by harmonic balance method is made based on the qualitative analysis of the types of fixed points and the existence of periodic motion. And the approximate periodic solution is obtained. Final-ly, the approximate analytical results are verified by numerical simulation. The results show that the analytic results are close to the numerical ones in accord with the qualitative analysis when the wind speed is in a certain region of parameter. Here, the results in this paper are valuable in the calculation of vibration engineering and theoretical design, since the long - time periodic oscillation is likely to cause the fatigue of structure, even probably effect se-verely the structural safety of bridge.