Nonlinear time-delay feedback control of a suspended cable under temperature effect

Abstract

In engineering, controlling the vibration of suspended cables is crucial and urgent. Notably, prolonged exposure to varying temperatures alters the vibration characteristics of suspended cables, impacting the selection and effectiveness of control strategies. Given the advancements in temperature-sensitive materials and refined engineering needs, researching temperature effects on cable vibration control is essential. Consequently, this study explores the nonlinear vibration control of suspended cables under temperature variations using a time-delay velocity feedback strategy. A nonlinear dynamic model of time-delay vibration considering temperature effects is established based on Hamilton’s principle. Comparative analysis quantitatively characterizes how temperature variations affect the inherent properties, nonlinear dynamics, and control strategies of suspended cables. Using the method of multiple scales, this study obtains analytical solutions for the primary resonance response. Analysis of three critical variables, sag-to-span ratio, control gain, and time delay under temperatures of $-40{}^{\circ }$C, $0‘{}^{\circ }$C and $+40{}^{\circ }$C led to an optimal control parameter design that achieves a vibration control efficiency of 93.6$\text{\%}$, underscoring the effectiveness of the time-delay feedback strategy.