Analytical solution of parametrically induced payload nonlinear pendulation in offshore lifting

Abstract

This paper presents a concept of analytical modelling methodology of a parametrically induced payload pendulation. A nonlinear analytical approximated solution was found for the considered 3-DOF model by simplifying to an elliptically excited Mathieu oscillator. The dynamic responses of the parametric pendulum being excited by bidirectional regular waves applied as kinematic functions at the crane tip were studied by means of the perturbation method.In order to investigate the model’s dynamic properties, an analytical first order solution was formulated through the utilisation of multiple-scale analysis. The accuracy of the solution derived was validated for two scenarios — payload oscillations outside the resonant region and on the resonance curve. The approximate analytical solution was examined for different sets of the system excitation curve parameters.The authors conducted numerical analyses (direct integration of a nonlinear governing equation) in order to give a satisfactory confirmation of the proposed methodology and evaluate the robustness of the obtained solution.Using the first order approximation, the results are found to be more conservative comparing to the simulations however, for all of the presented cases, the solution achieves a very good correspondence with the numerical results. The studies were summarised with an examination of the stability assessment of the lifted object.