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In this paper, a mathematical model is presented to numerically simulate the dynamical responses in a multi-cable suspension platform taking into account the slack cables and guiding devices. The state change of the cable (slack versus tensioned) is considered and is described mathematically by a complementary condition equation, and the interactions between the guiding wheels and the shaft wall are described by the Heaviside step function. The Lagrange's equation with constraints is used to derive the dynamic equations of the system, and a non-smooth generalized-α algorithm for non-smooth phenomena of multibody dynamics is applied to numerically solve the equations. The simulation results have shown the dynamic responses of the platform and the cable tension characters when different cables are excited by different longitudinal excitations. Moreover, the results have illustrated how the cable tension differences may affect the pressure on the shaft wall applied by the guiding devices. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The dynamic responses of cable-driven parallel sinking platform are investigated considering the longitudinal–torsional coupled characteristics of the cable. The dynamic equations of the system are derived through the Lagrange equations, and the geometric matching conditions and the constraint forces at the interfaces between the cables and the platform have also been considered in the equations through Lagrangian multipliers. By neglecting the slack state of the cable, the numerical results of the mathematical model are obtained through Newmark-beta method after transforming the derived differential algebraic equations (DAEs) to a system of ordinary differential equations (ODEs). An ADAMS simulation is carried out, and the ADAMS simulation results agree well with the results obtained through Newmark-beta method. The results have shown that the lateral characteristics of the cables have a great effect on the torsional vibration of the platform, and by arranging the cables correctly will help to reduce the rotation of the platform. [ABSTRACT FROM AUTHOR]