Static and dynamic stiffness in the modeling of inclined suspended cables

Inclined suspended cables (ISCs) have several applications in the transmission lines of power network systems. This study attempts to simplify the modeling of ISCs by addressing their static and dynamic stiffness. The dynamic problem of a uniform damping ISC under a harmonic excitation is studied under the assumptions that the suspended cable is deflected in a parabolic profile during static equilibrium and all the displacements in the dynamic in-plane motion are small. A closed expression for the frequency response function (FRF) is derived, based on which the static stiffness of the ISC is established; this aids in modifying the Ernst's formula. Furthermore, the cable dynamic coefficient is defined by considering the participation factors and the minimum number of vibration modes. The dynamic stiffness of the ISC is established by combining the static stiffness and cable dynamic coefficient. In addition, a shaking table test of a reduced-scale tower-line system model is performed to verify the correctness of the finite element model of the suspended cable. The results of the static and dynamic analyses indicate that the spring model based on the dynamic stiffness, showing a good precision, has a higher computational efficiency compared with the suspended cable model. Finally, the spring model, which is applied to the tower-line system by choosing different seismic excitations, inclinations, sag-to-span ratios, and spans of ISCs, is valid for an arbitrary angle of inclination ranging between 0° and 50°. Moreover, its results are in very good agreement with those of the suspended cable model.