Dynamical analysis of a stay cable with a nonlinear energy sink and time-delayed feedback control

• Published in: Engineering structures 2024-07, Vol.310, p.118074, Article 118074
• Main Authors: Liu, Zhiqun, Mao, Xiaochen
• Format: Article
• Language: English
• Subjects: Bifurcations; Frequency responses; Nonlinear energy sinks; Stay cable; Time-delayed feedback control; Vibration reduction
• ISSN: 0141-0296
• DOI: 10.1016/j.engstruct.2024.118074

Stay cables exist commonly in engineering and can exhibit sustainable and large vibrations under external excitations. The unexpected oscillations always lead to the fatigue and damage of structures, resulting in the economical loss. This paper studies the vibration control of a stay cable system with a nonlinear vibration absorber and time delay control. The governing equations of motion of the stay cable system under harmonic excitations are given. The stability and different bifurcations of the trivial equilibrium point of the system are analyzed. The bifurcation diagrams with respect to the control parameters are illustrated. The frequency responses of the forced system are obtained by using the harmonic balance method. Numerical simulations are performed to validate the obtained results and various dynamical phenomena are shown, such as the multi-period oscillations, quasi-periodic responses and chaotic motions. The effects of the time-delayed feedback control on the nonlinear dynamics and vibration reduction of the system are extracted. It is shown that the proper values of the time delay and feedback gain can improve the vibration reduction performance of the system, such as the suppression of the resonance peaks and elimination of the complex responses. •A time-delayed nonlinear vibration absorption system is presented for the control of stay cable.•The stability and different bifurcations of the equilibrium points of the stay cable are analyzed.•Abundant and interesting responses of the nonlinear delayed stay cable are shown.•The effects of the time delay and control gain on the system performance are explored.