Spectral Analysis of a Sagged Cable with an Optimal Viscous Inertial Mass Damper under Random Wind in a Generalized State-Space Formulation

Abstract

In this study, a spectral analysis method is proposed for a sagged cable with an optimal viscous inertial mass damper (VIMD) under random wind loads based on a generalized state-space formulation. The frequency response functions of the cable responses were evaluated for the wind force vector using complex modes orthogonal to the system matrices, from which the power spectral densities of the cable responses were readily obtained for the spectral matrix of the wind force. The accuracy and efficiency of the proposed method were verified by comparing the root mean square responses with those obtained from the time-domain and covariance analyses. The performance of two VIMDs optimized by the fixed-point method and the maximum damping ratio method was investigated for various cases of cable sag and wind properties. Serviceability failure probability analysis was also conducted using the first-passage problem. The results show that the proposed spectral method is computationally more efficient than the other two analysis methods. The VIMDs optimized for the first original cable mode were found to be highly effective in reducing cable vibration and the probability of serviceability failure.