A highly precise frequency-based method for estimating the tension of an inclined cable with unknown boundary conditions

This paper develops a method for precisely determining the tension of an inclined cable with unknown boundary conditions. First, the nonlinear motion equation of an inclined cable is derived, and a numerical model of the motion of the cable is proposed using the finite difference method. The proposed numerical model includes the sag-extensibility, flexural stiffness, inclination angle and rotational stiffness at two ends of the cable. Second, the influence of the dynamic parameters of the cable on its frequencies is discussed in detail, and a method for precisely determining the tension of an inclined cable is proposed based on the derivatives of the eigenvalues of the matrices. Finally, a multiparameter identification method is developed that can simultaneously identify multiple parameters, including the rotational stiffness at two ends. This scheme is applicable to inclined cables with varying sag, varying flexural stiffness and unknown boundary conditions. Numerical examples indicate that the method provides good precision. Because the parameters of cables other than tension (e.g., the flexural stiffness and rotational stiffness at the ends) are not accurately known in practical engineering, the multiparameter identification method could further improve the accuracy of cable tension measurements.