斜拉桥中斜拉索的面内外耦合内共振分析

研究了桥面侧振引起的斜拉索非线性振动问题。基于Hamilton原理建立了拉索的非线性振动控制方程,并利用多尺度法得到了斜拉索振动方程的二阶近似解。通过具体算例分析了斜拉索面内一阶模态与面外一阶模态相互耦合发生内共振的可能性,讨论了拉索倾斜角对拉索振动的影响,比较了在零初始条件和非零初始条件下拉索振动响应的区别。研究发现:拉索内共振发生在一定的激励频率和激励幅值区域内;改变倾斜角度,会影响拉索发生内共振时激励频率区域的大小;初始条件的不同,拉索的振动形式会相差很大。

Internal resonance analysis because of in-plane and out-of-plane coupling effects of the stay cable in the cable-stayed bridge

A new model for non-linear vibration analysis of the stay cable is built,which considers the coupling effects between the cable and the bridge.The effects of the lateral vibration of the bridge to the stay cable are included herein.The vibration equation of the stay cable is derived based on the Hamilton theory and solved by the multiple scales method.Through the analysis of a real stay cable,the possibility of internal resonance because of the coupling effects between the in-plane first mode and out-of-plane first mode of the cable was determined.Then the effects of the inclined angle on the vibration were also discussed in details.Finally,the responses of the cable under different initial conditions were compared.It is found that the internal resonance happens when the excitation frequency and amplitude are in a certain range.The range of excitation frequency needed for the happening of the internal resonance will be affected by the inclined angle and the form of vibration of the cable is determined by the initial conditions.