斜拉桥单梁-多索模型的非线性振动

Multi-cable stayed beam model and nonlinear vibration analysis of cable-stayed bridge

建立斜拉桥的单梁-多索力学模型,考虑其初始垂度、大位移而引起的几何非线性因素的影响,同时考虑拉索与桥面连接条件和边界条件的影响,通过Hamilton原理建立单梁-多索的面内非线性振动方程。利用Galerkin方法将非线性偏微分方程转化为关于时间的二阶常微分方程组,以单梁-双索为算例,在桥面对拉索的参数激励条件下,利用Runge-Kutta法对拉索之间的相互作用进行数值分析。研究结果表明:当2根索的频率比约为1时,索与索之间通过桥面运动产生能量传递,可使拉索的大幅振动更加强烈。

Multi-cable stayed beam model of cable stayed bridge was established. Based on Hamilton＇s principle, the in-plane nonlinear governing equations of cables and beam were derived, in which the static sag and the geometric nonlinearity of the cable were considered and the simple connection condition and boundary condition of the cable and deck were taken into account. Furthermore, Galerkin＇s method was used to convert the partial differential equations into the ordinary differential equations, and the Runge-Kutta method was introduced to solve the equations. The numerical results of two cables stayed beam structure show that energy transfer between cables by movement of deck exists and may lead to larger vibration of cables on the condition that the lower natural frequencies of cables are close to each other.