No abstract

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 ( l1/ l = 2%, l2/ 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 ( l2/ l1) should be near 2. The optimized ratio of the damping coefficients ( η1/ η2) should be lower than l2/ l1, and the lower limit of η1/ η2 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 40th ∼ 50th modes.

The trial-and-error method is complex and tedious, but often adapted to determine the cross-section sizes of core beams in the design of reduced-scale models. In this study, two optimization methods, the optimization methods in ANSYS and the genetic algorithm, are investigated to optimize the cross-section sizes of core beams of reduced-scale models, which centers around two targeted moments of inertia and a targeted torsion constant. Due to the difficulty of obtaining an analytical solution of the torsion constant, a series of numerical solutions are proposed. Then, taking a U-shaped cross section as an example, the four geometric sizes of the section are optimized by the ANSYS optimization method and the genetic algorithm, respectively. The results of both methods are in good agreement with the targeted values, but the ANSYS optimization method is prone to fall into the local optimization zone and hence could be easily affected by the initial values. The shortcomings of the ANSYS optimization method can be easily avoided by the genetic algorithm, and it is easier to reach the global optimal solution. Finally, taking a suspension bridge with a main span of 920 m as a prototype, the full-bridge aeroelastic model is designed and the genetic algorithm is used to optimize the cross-section sizes of core beams in the bridge tower and the deck. Natural frequencies identified from the aeroelastic model agree well with the target ones, indicating the structural stiffness, which is provided by the core beams, has been modelled successfully.