Calculation of Floating Crane Natural Frequencies Based on Linearized Multibody Dynamics

Natural frequencies and modes of a floating crane with a suspended load are studied. Both the floating crane and the suspended load are modeled as rigid bodies with six degrees of freedom. The suspended load is considered to be partially immersed in the sea water. A wire rope for load suspension is assumed to be non-extensible and without bending stiffness. Linearized governing equations for a coupled dynamic response are derived based on the multibody system dynamics with small displacements assumption. An added mass for the floating crane as well as the partially immersed load is determined using traditional potential theory and tree-dimensional boundary element method (in a frequency domain). Mapping from the frequency to the time domain is necessary to determine the correct added mass value for calculating above described natural frequencies and modes. A damping of the overall system can be calculated as some small portion of a critical damping. A numerical example is based on the floating crane during positioning of precast concrete piles. These piles are main part of foundations for over sea bridges.