Abstract
The effects of time delays on the primary parametric vibration of controlled stay cables under axial excitation were studied. In view of cable sag and geometric nonlinearity, the nonlinear parametric vibration equation for the controlled stay cable system under axial excitation was built based on the Hamiltonian principle. Then the dynamic system with time delay was formulated by means of the Galerkin method. The multiscale method was used to analyze the primary parametric resonance of the controlled stay cable system and obtain the effects of different time delays and control gains on the time histories of the parametric vibration and the stability region of the controlled stay cable. The study shows that time delay weakens the vibration controlling effects on the stay cable, and the stability region of the parametric vibration is shifted. The larger the time delay is, the worse the controlling effects will be. The work plays a guiding role in the parametric design of the control system for stay cables.
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