Force method of ship hull vibration analysis

Abstract

Many numerical methods--transfer matrix, finite difference and finite difference and finite element methods--which take piece-wise account of the variation of the input-datas over the length of the ship hull, such as area, weight, etc., are now available. Most of these methods give deflection and rotation as output in the eigenvalue problem or in the modal analysis, from which vibratory bending moments and shear forces for given exciting forces and moments are obtained after numerical differentiation of deflections and rotations of cross-sections. In order to avoid this numerical differentiation after the modal analysis, the force method can be employed, instead of the usual deformation method, for improved accuracy in ship hull vibration analysis. In this paper, the necessary differential equations of vibrations are derived and analogies between the force method and deformation method are established so that the existing programs in deformation quantities can be used. Moreover, the eigenfunctions of shear force and bending moment and the envelopes of their maximums for an impact force and moment under vertical vibrations are presented for an ice-going ship.