Coupled flexural and torsional vibrations of ship-like girders

The paper is related to investigation of coupled horizontal flexural and torsional vibrations of container vessels. Differential equations of coupled vibrations of a prismatic beam with open cross-section are derived. The equations are solved analytically by direct integration and by variational method. In the former case, the frequency equation is reduced to a polynomial of the fourth order. In the latter case, beam deflection and twist angle are assumed in the form of series of natural modes of uncoupled vibrations of free beam with suspended warping. The variational method manifests very fast convergence and high accuracy. Application of the developed methods is illustrated in the case of a prismatic pontoon with cross-section of a container vessel. The same numerical example is used for checking 1D FEM mathematical model and code developed for analyses of real structures of container vessels with variable cross-sections. In addition, correlation analysis of 1D and 3D FEM results is done to validate the accuracy of the former.