Speaker
Description
Ropes are used in modern structures as load-bearing elements for various applications, e.g. the main cables or cross-ties in cable-stayed bridges, cable roof structures, or high-voltage transmissions lines. Guy lines are designed to stabilize the structure and keep it in the right position against external loads.
Since the ropes do not transfer compressive forces, they require significant pre-tension forces to operate properly. However, even if the pre-tension force is very high, due to the significant lengths of the guy lines, a sag of the rope is observed under the action of its own weight. Therefore these elements should be analyzed at least as cables with a small sag. Due to significant dimensions, and slenderness guyed towers are very sensitive to dynamic excitations such as earthquakes. The flexibility of the structure leads to significant deformation of the tower under dynamic loads, which in turn leads to the excitation of the guy lines. Since earthquakes are burdened with high uncertainties, the vibrations caused by this type of loads should be analyzed by using stochastic methods.
The subject of considerations is a simplified model of a tower treated as a cantilever pole with a single guy line, modelled as a small-sag cable, attached to the structure at a certain height and anchored to the foundation at the other end. Due to position of the cable in the considered system, it is excited by two sources due to the seismic loads: by ground motions at the point of rigid attachment of the cable in the foundation and by displacements of the tower resulting from its bending deformations at the point of anchoring the cable. The Gaussian white noise process is used for simplified modelling of the earthquake ground motions. The Ritz method and Lagrange’s equations are used to obtain the non-linear system of differential equations of motion where the coupled longitudinal and lateral vibrations are observed. In previous works, the authors considered the system simplified to a single (fundamental) mode approximation. However, in real systems the vibration results from the superposition of the responses in different modes. Therefore, in the proposed approach, the multimodal response of the system is considered in order to take into account the influence of the selected modes on the obtained results. The mean values and variances of particular random state variables are obtained by using the equivalent linearization technique and verified against Monte Carlo simulations.
