Universal Characteristic Frequency Equation for Cable Transverse Component System and Its Universal Numerical Solution

It is meaningful to develop an accurate universal approach to solve the dynamical characteristic problem of a cable system combined with additional components used in real engineering. A segmented dynamic governing equation is presented for a taut shallow cable supported in the middle by a transverse component. Then, a universal frequency characteristic equation is proposed that considers all the influence factors, including the flexural rigidity, sagging, inclination angle, finite rigidity or damped boundary condition, and the intermediate supporting component. A general numerical solution is presented by giving an analytical derivative expression for the dynamic stiffness of the cable system. As a result, the modal parameters of an arbitrary complicated cable system can be obtained via the root of the equation. Finally, the accuracy of the proposed approach is verified using numerical cases, and its validity is also proved by applying it to case studies of several typical cable systems.