The natural frequencies and mode shapes of the horizontal-and-torsion-coupled vibrations of a ship hull with large hatch openings were investigated using the finite-element method; the dynamic behavior of the ship hull due to excitation of regular waves was studied by means of the Newmark direct integration method. In order to determine the property matrices of the entire ship hull, the hull was considered a nonuniform free-free beam composed of various open-and close-sectioned thin-walled tubes. Then the elemental mass matrix and stiffness matrix of each beam segment were derived based on the relationship between the kinetic energy and the nodal velocities and on that between the potential energy and the nodal displacements of each beam segment, respectively. The assembly of the elemental mass matrices and stiffness matrices will give the overall property matrices of the entire ship hull. In the forced vibration analysis, attention was paid to the influence of the responses of the heading angle, ship speed, and some key parameters relating to the structural properties. Also considered in this study were the effects of warping torsion, shear deformation, rotatory inertia, shear center and centroid, which are not concurrent, and the shear centers of various cross sections that are not collinear.
Analysis of Wave-Induced Horizontal-and-Torsion-Coupled Vibrations of a Ship Hull
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Wu, Jong-Shyong, and Chian-Sen Ho. "Analysis of Wave-Induced Horizontal-and-Torsion-Coupled Vibrations of a Ship Hull." J Ship Res 31 (1987): 235–252. doi: https://doi.org/10.5957/jsr.19188.8.131.52
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