Finite element analysis of coupled vibration for hoisting cable with time-varying length

The coupled axial-torsional responses of the hoisting cable with time-varying length are investigated in order to predict the longitudinal vibration more accurately. The equations of motion are formulated by Hamilton’s principle and the finite element method (FEM), in which a variable-length cable element is introduced. In order to validate this theoretical model, an ADAMS simulation model is established in the framework of the multi-body system dynamic. The result shows that the numerical solution is in reasonably good agreement with the ADAMS simulation. The frequencies of the cables with the coupling considered and neglected are analyzed by varying the excitation frequency, which indicates that the coupling effect reduces the natural frequency of the cable and the maximum amplitude shifts from the resonance region to the deceleration stage as the coupling coefficient increases.