The Research On Mechanism Of Double Strands Wake Galloping Of The Long-span Flexible Bridge

In recent 30 years,more and more bridges arose all over the world.The span of the cable-supported bridges(include suspension bridges and cable-stayed bridges)became longer and longer.Due to light mass,low frequency and small structural damping,the hangers(or cables)are prone to a variety of wind induced vibration,Large amplitude vibrations of the hangers on several suspension bridges in field observations were found,for example,the Akashi Kaikyo Bridge in Japan,the Xihoumen Bridge in China,and the Great Belt East Bridge in Denmark.These kinds of wind-induced vibrations of the hangers will lead to the fatigue damage of the bridge,the uncomfortable of the users,and may increase the possibility of traffic accident.There might be several different mechanisms for the wind-induced vibrations of the hangers of the suspension bridge.The motivation of the research in this paper is the aerodynamic interference between multiple strands.It could be found from field observation that the windward strand always keeps static while the other strands in the wake vibrate one after another.Therefore,the instability mechanism of multiple strands(over 2)could be investigated by simplifying as a double strands model.This model can also be applied to the two parallel stay cables in the cable-stayed bridges.The main contents in this paper are as follows.(1)Two smooth circular cylinders models were made to simulate the double strands.A series of wind tunnel tests were carried out to measure the aerodynamic force on the leeward strand.The spatial distributions of the mean drag coefficient CD and the mean lift coefficient CL of the wake strand were obtained.Based on the experimental results,the instable region of wake galloping of the leeward strand was carefully studied by utilizing the Routh-Hurwitz stability criterion.The results showed that the mean drag coefficient of the leeward strand is symmetrical concerning the centerline of the wake,whereas the mean lift coefficient is antisymmetrical.The mean drag and lift coefficients both change sharply within the distance of 2 times of the hanger diameter from the wake centerline.The instable region of wake galloping of the leeward strand appears to be a strip shape with a width of one times of the hanger diameter,and distributes symmetrically on both side of the wake centerline.(2)Based on the quasi-steady theory,the theoretical analysis model were established for wake galloping of the hangers of the suspension bridge.By utilizing the Runge-Kutta method,the response of the leeward strand was numerically analysed.The results show that:(1)Above the wake centreline,the leeward strand moves in a clockwise direction,and the angle between the main axis of the trajectory and the along-wind direction is obtuse.Under the wake centreline,the leeward strand moves in a counterclockwise direction,and the angle between the main axis of the trajectory and the along-wind direction is acute.(2)The frequency of the oscillation of the leeward strand is significantly small than the natural frequency of the leeward strand,which indicates that there exists an obvious negative aerodynamic stiffness.(3)The natural frequency of the leeward strand has a significant influence on the wake galloping.if the natural frequencies in two degree-of-freedom are identical with each other,the response of the wake galloping of the leeward strand could be well mitigated by increasing the natural frequency of the leeward strand.However,if the natural frequencies in two degree-of-freedom are not identical with each other,the instability region of wake galloping of the leeward strand becomes more narrow.(3)By utilizing an algorithm based on physical connotation of aerodynamic force,the aerodynamic force on the leeward strand and each component of it were studied quantitatively.The results show that the steady aerodynamic force is about an order of magnitude more than the aerodynamic stiffness force and the aerodynamic stiffness force is about an order of magnitude more than the aerodynamic damping force.The aerodynamic stiffness coefficient is about 3% to 10% of the structural stiffness coefficient.The aerodynamic damping coefficient is about 5 times of the structural damping coefficient.(4)The instability mechanism of wake galloping of the leeward strand was studied by analyzing the energies inputted.The results show that the work done by the aerodynamic damping force and the structural damping force is always negative.If the positive work induced by the aerodynamic stiffness force is equal to the negative work induced by the aerodynamic damping force and the structural damping force,the wake strand will maintain a stable limit cycle movement.(5)By using forced vibration system,a series of wind tunnel tests were carried out to identify the aerodynamic derivatives of the leeward strand.The characteristics of the aerodynamic stiffness were obtained,and were compared with those obtained from theoretical analysis.