Modal Characteristics-based Identification Of Cable Tension With Unknown Boundary Condition

Because of the light weight and high strength, cables, with a high mechanical efficiency, are widely used in cable-supported bridges to achieve the pursuit of large span. Identification of the cable tension is essential for assessment and monitoring of the health condition of the cable-supported bridges. At present, the vibration-based methods, using string theory or beam theory and assuming that the cable is simply supported or fixed at both ends are commonly use in practice. Actually, the boundary conditions of cable are more complex than we might imagine. Since the difference between various restraint devices and systems, the real boundary condition is more likely unknown. With unknown boundary condition, there is no solution for the vibration equations no matter using string theory or beam theory. Besides, sag effect is significant for the natural frequency of cable, especially for fundamental frequency. The identification of cable tension by using vibration parameters with unknown boundary condition is the research hotpot recently.Based on the above problem, this paper first brings out the basic theory of vibration-based methods, and analyzes the influence of boundary conditions on tension estimation. By assuming the general boundary conditions of cable and using the natural frequency and the corresponding dynamic measurements from several sensors along the cable, this paper then analyses the modal characteristics of string model and beam model with or without sag respectively, and finally estimating the axial force as well as the tanslational and rotational stiffness at both element ends. It can indicated from the research results that for string model and beam model with ζ less than 50, this method is applicable for the cable tension and boundary stiffness identification without the consideration of sag effect. For cables with the sag effect, good results can be reached by using anti-symmetric mode shapes. Although there is no analytical solution for cable tension according to this method, it is simple and easy to master compared to other analytical methods. For cables with unknown boundary conditions, this method shows its special value and significance.