The lateral response of the moving hoisting conveyance in cable-guided hoisting system is investigated in this paper. The equations of motion are derived by Hamilton's principle while the equivalent mass and stiffness of the guide cables are formulated. Galerkin method is employed to transform the governing equation into a set of ordinary differential equations. Subsequently, an ADAMS simulation model based on multi-degree of freedom is established to validate the theoretical model. Meanwhile, a high-efficiency simulation approach is proposed, in which the contact force is replaced with fixed joints and distance sensors. The numerical solution for equations set is obtained using Newmark-β method and the convergence of the solution is discussed, then the presented theoretical model is compared with the previous models describing the rigid rail-guided hoisting system. The results indicate that the numerical simulations are in reasonably good agreement with the ADAMS simulations and this presented model includes the previous models. The influence of parameters on the lateral response is analyzed, which reveals the maximum lateral displacement is linearly proportional to the excitation amplitude. Also, the appropriate preload can be determined by the theoretical model, which is beneficial for vibration control.

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.

The flexibility of the guiding rope and the tension difference between two guiding ropes cause the lateral and torsional vibrations of the hoisting conveyance in the rope-guided hoisting system, respectively, which are theoretically investigated with two different cases in this paper. The assumed modes method is used to discretize the hoisting rope and two guiding ropes, and Lagrange equations of the first kind is adopted to derive the equations of motion, while the geometric matching conditions at the interfaces of the ropes are accounted for by the Lagrangian multiplier. Considering all the geometric matching conditions are approximately linear, the differential algebraic equations are transformed to a system of ordinary differential equations. The current method can obtain not only the accurate lateral displacements of two guiding ropes, but also the constraint forces between the hoisting conveyance and two guiding ropes. Further, the current method is verified by the ADAMS simulation. Finally, the effects of various parameters on the lateral and torsional vibrations of the hoisting conveyance are analyzed and results indicate that the appropriate tension difference and distance difference could decrease the maximum lateral displacement, which is useful to design super deep rope-guided hoisting system for the decrease of the vibration.