斜拉桥拉索风雨激振的两质量三自由度理论模型

A theoretical model of rain-wind induced vibration of stay cables:a coupled two-mass oscillators with three degree-of-freedoms

斜拉索的风雨激振严重地影响到斜拉索以至于斜拉桥的安全,其机理至今仍无定论。同时考虑拉索面内和面外两个自由度,并假设拉索和水线之间的作用力为库仑阻尼力和线性阻尼力,建立斜拉桥拉索风雨激振的两质量三自由度理论模型。采用Runge-Kutta法对拉索和水线的耦合方程进行数值求解,得到拉索和水线的运动规律。与仅考虑拉索面内自由度的两质量两自由度理论模型相比,考虑拉索面内面外自由度的两质量三自由度理论模型的起振风速区更多,这主要是因为拉索的水平气动力系数也存在突降,且拉索面内面外运动是相互耦合的。水线上的气动力和重力为水线提供总体的平衡;阻尼力则消耗水线的能量;至少一个方向的拉索运动引起的附加惯性力(竖向或水平)一直对水线做正功。

Rain-wind induced vibration of stay cables severely affects the safety of cable-stayed bridges, but unfortunately, up to now the mechanism is still unclear. Assuming the interaction between rivulet and cable surface to be a coulomb damping force and a linear damping force, a new theoretical model of rain-wind induced vibration is established. The presented model includes two cable degrees-of-freedoms （in-plane and out-of-plane） and one rivulet degree-of-freedom. Runge-Kutta method is used to solve the set of equations, and the responses of cable and rivulet are obtained. Comparing with the model in which only the in-plane degree-of-freedom of a stay cable is included, the present model allows rain-wind induced vibration to take place within more wind velocity zones. This is because a sudden decrease also exists in the horizontal aerodynamic force coefficient of a stay cable, and the in-plane and the out-of-plane vibrations are coupled with each other. Whether the rivulet steadily exists on the upper surface of a stay cable depends on the balance between aerodynamic force and gravity. Additional inertia force due to the motion （inplane or out-of-plane） of the cable supplies energy for the motion of the rivulet, and the damping force between rivulet and cable surface dissipates energy to stabilize the rivulet.