Effectiveness of damping and inertance of two dampers on mitigation of multimode vibrations of stay cables by using the finite difference method

Stay cables of several cable-stayed bridges with a span of nearly 1000 m are confronted with the simultaneous actions of low-mode rain-wind induced vibration and high-mode vortex-induced vibration. It is difficult to effectively reduce these two kinds of cable vibrations by installing one damper at the end of the stay cable. In this paper, the effectiveness of two dampers attached at the lower end of the stay cable, including viscous dampers and viscous inertial mass dampers, is investigated by the finite difference method. First, the stay cable was simplified as an inclined cable with sag, and equation of motion governing the stay cable attached with two dampers was derived. This equation was then numerically solved by the finite difference method. Second, taking Cable A30 of the Suzhou-Nantong Yangtze River Bridge as a reference, a series of numerical simulations were carefully conducted to obtain the damping ratios of the first fifty modes. The results show that it is impossible to enhance the damping ratios of all of the concerned modes up to the minimum target value only by installing a single viscous damper or a single viscous inertial mass damper at the end of the stay cable. However, two viscous dampers installed at the lower end of the cable (l(1)/l = 2%, l(2)/l = 5%) can overcome the shortcoming of a single viscous damper or viscous inertial mass damper to enhance the damping ratios of the first 34 modes up to the minimum target value (0.5%). In general, the optimized relative location of the two dampers (l(2)/l(1)) should be near 2. The optimized ratio of the damping coefficients (eta(1)/eta(2)) should be lower than l(2)/l(1,) and the lower limit of eta(1)/eta(2) is determined by the minimum target values for modal damping ratios. Moreover, it appears that a lower installation position of two viscous dampers can realize the mitigation of higher modes even up to the 40(th) similar to 50(th) modes.