Non-Linear Vibration and Dynamic Fracture Mechanics of Bridge Cables

Abstract: In the present work, the non-linear vibrations and the corresponding dynamic fracture mechanics of cables of cable-stayed bridges are studied. The cables are among the most critical components in cable-stayed bridges and there are different damage sources such as corrosion, vibration, fatigue and fretting fatigue that can significantly affect them, thereby reducing the cable’s service life and even producing their failure. Cable-Parametric Resonance is the specific non-linear vibration studied in this research. This type of vibration occurs due to displacements presented at the cable supports. These displacements are induced by the wind and traffic loads acting on the pylon and deck of the bridge. Under certain conditions, unstable cable-vibration of significant amplitude can be registered. Therefore, numerical and experimental analyses are carried out in order to describe this phenomenon and to determine the corresponding instability conditions. Two non-linear models of cable-parametric resonance are studied to predict the cable response. In the simulation method, the non-linear components are treated as external forces acting on the linear systems, which are represented by Single Degree of Freedom systems and described by digital filters. A clear non-linear relationship between the excitation and the cable response is observed in the simulations and the experiments. The corresponding experimental analysis is based on a scaled model (1:200) of the Öresund bridge and a good agreement between the numerical and experimental results is found. After obtaining the relationship between the cable response and the excitation, the cable instability conditions are determined. This is done by finding the minimum displacement required at the cable supports in order to induce nonlinear cable vibration of considerable amplitude. The instability conditions are determined within a wide range of excitation frequencies and conveniently expressed in a simplified and practical way by a curve. The determination process is rather fast and offers the possibility to evaluate all bridge cable stays in a rather short time. Finally, the dynamic fracture mechanics of the cable is considered by studying the fracture toughness characteristics of the material under dynamic conditions. Finite Element simulations on a pre-cracked three-point bending specimen under impact loading are performed. The observed cable instability is equivalently considered as the associated response to impact load conditions, and a crack as a defect on the wires of a cable stay. The simulations are based on an experimental work by using the Split Hopkinson pressure bar (Jiang et al). The dynamic stress intensity factor KI(t) up to crack initiation is then obtained by different methods. The numerical estimations based on the specimen’s crack tip opening displacement (CTOD) and mid-span displacement were closest to the experimental results. It is observed that a better estimation of the dynamic stress intensity factor relies on a proper formulation of the specimen’s stiffness.