Non-linear Dynamic Response of a Small-sag Cable Model of a Guy Line of a Guyed Tower to Stochastic Wind Excitation

A cable with small-sag is considered as a simplified model of guy line of a guyed tower. The strong dynamic wind action leads to the transverse vibrations of the guyed tower that causes the base-motion excitation of the cable and its axial and lateral vibrations. Because of strong gusts of wind the significant displacements of the tower can be observed, wherefore the geometrical non-linear effects arise. In the considered model the axial non-linear vibrations of the cable with small-sag are coupled with transverse ones. The set of ordinary differential equations is obtained by using the Galerkin method. The single-fundamental-mode response of the tower to a wide-band stochastic wind excitation is considered as the narrow-band stochastic process. Therefore the base motion excitation for the guy line is assumed as an idealized response of an auxiliary linear filter to a Gaussian white noise excitation. The obtained state vector of the system is expressed by the original state variables augmented by the filter state variables. The equivalent linearization technique is then used to convert the original non-linear system into the equivalent linear one with coefficients obtained from the condition of minimization of the mean square error between the both systems. As a result the mean values, variances and cross-covariances of particular random state variables are determined and verified by Monte Carlo simulation.