Nonlinear resonant responses of suspended cables with a longitudinal time-delayed feedback control

In this study, the vibration control of suspended cables is achieved through the implementation of a longitudinal time-delay feedback control strategy. Based on the Hamilton’s variational principle and using boundary conditions, the motion differential equations for the suspended cable under longitudinal velocity and acceleration time-delayed feedback control are derived. The delay differential equations are discretized using the Galerkin method. The fourth-order approximate solution for the primary resonance response of the suspended cable under time-delayed feedback control is obtained using the method of multiple scales. The correlation between the system response and the controlled parameters is established, and the vibration control effects under different control parameters are analyzed through numerical examples.