Accurate Tension Identification Of Cable With An Intermediate Support

The vibration frequency method based on the string vibration theory is widely used in the construction control, state evaluation and health monitoring of the cable structures since it is economical and convenient. However, the string vibration theory ignores the effects of nonlinear factors such as flexural rigidity, sag, boundary condition of the cable and intermediate supports, and sometimes these factors will bring unacceptable error in the practical applications. When these nonlinear factors are taken into account, nonlinear vibration of cables is difficult to deal with. In order to fully prove the dynamic characteristics of the cable, it is very important to solve the vibration problem which is based on nonlinear vibration theory. So this paper puts forward four methods to solve nonlinear vibration problems of the cable, the maincontent as follows: (1) The vibration function of the cable considering the effects of flexural rigidity and intermediate support (damper) is directly solved by the analytic method, and the eigenvalue equation is obtained which is also a transcental equation. After simplification, a dimensionless expression for frequency eigenvalue is explicitly obtained as well as cable tension.(2) When the vibration equation of the cable which considers the effects of flexural rigity and sag is established, an asymptotic expression in the form of small parameter series for frequency eigenvalue is derived by using singular perturbation method. The cable tension can be calculated from frequency eigenvalue equation.(3) Takeing the effects of flexural rigity, sag and damper of the cable into account, an expression for cable tension is derived by energy method. According to the assumptions, the application scope as well as the effects of factors mentioned before should be discussed combined with FEM method.(4) The deviation between the design parameters and true parameters led to the value of the cable tension existing system error. This paper put forward identification method with model and without model respectively, combining with PSO particle swarm method. Single parameter identification method and multiple parameter identification method of key parameter were discussed as well. (5) Taking the dynamic test results of the Gan Xi Gou bridge and the Hai Yin bridge into the formulas for the four mian methods as case study, we could check the accuracy of the cable tension calculated by the practical formulas.