Modelling and passive control of flexible guiding hoisting system with time-varying length

A coupled dynamic modelling of the flexible guiding hoisting system is established, which includes the transverse-longitudinal-coupled vibration and the rotational vibration. Substituting vibrational energy of the system into Hamilton principle and applying the dynamic constraint, a distributed parameter mathematical model of the multi-rope system is derived. It is governed by coupled partial differential equations and ordinary differential equations (PDEs-ODEs), where the dynamic constraint in the form of an unknown moving force is the only connection between the hoisting conveyance and the guiding ropes. Based on Galerkin method, the dynamic response of the system is validated by numerical calculation and ADAMS simulation. Besides, an absorber with artificial intelligence optimization is proposed to reduce system vibration. The simulation result has demonstrated that a hoisting conveyance resonance can be observed when the external disturbance frequency is close to the system natural frequencies. Moreover, a vibration absorber can effectively diminish the resonant peaks of the first three orders of the guiding rope.