Nonlinear Vibration Control of a High-Dimensional Nonlinear Dynamic System of an Axially-Deploying Elevator Cable

For the first time, a numerical study is presented to demonstrate the importance of high-dimensional nonlinear dynamic systems of axially-deploying elevator cables in the nonlinear vibration and control of such time-varying-length structures, especially under the condition of external disturbance. Firstly, a multi-dimensional nonlinear dynamic system of an axially-deploying elevator cable is established using Hamilton’s principle and the Galerkin method, and a large-amplitude vibration of the system is specified. Then, the established nonlinear dynamic system of the elevator cable is extended to account for external disturbance. Furthermore, an adapted fuzzy sliding mode control strategy is applied to suppress the specified vibration in the nonlinear dynamic system involving external disturbance. From numerical simulations, it is discovered that different dimensions are required for nonlinear vibration and control of axially-deploying elevator cables. The study provides guidance on nonlinear vibration and control of axially-deploying elevator cables in high-dimensional nonlinear dynamic systems.