An advanced theory of thin-walled girders with application to ship vibrations

The paper presents an outline of the advanced theory of thin-walled girders. The improvement includes shear influence on torsion as an extension of shear influence on bending. The analogy between bending and torsion is recognized and pointed out throughout the paper. Complete differential equations of coupled flexural and torsional vibrations for a prismatic girder are derived. In addition, the 8 d.o.f. beam finite element, utilizing the energy approach, is constituted with stiffness and mass matrices, and load vectors. The paper describes determining of geometrical properties of multi-cell open cross-sections by employing the strip element method. Numerical procedures for vibration analyses are outlined. Furthermore, dry natural vibrations of a VLCS (Very Large Container Ship) are analysed by 1D FEM model as a prerogative for hydroelastic analyses of these relatively flexible vessels. Influence of transverse bulkheads is taken into account by increasing torsional stiffness of the ship hull proportionally to their deformation energies. Validation of 1D FEM model is checked by correlation analysis with the vibration response of the fine 3D FEM model.