Coupled horizontal and torsional vibrations of a flexible barge

Differential equations of coupled flexural and torsional vibrations of a prismatic beam are derived. The equations are solved analytically by the direct integration and the Ritz method. In the former case, the frequency equation is reduced to a polynomial of the third order. In the latter case, beam response is assumed in the form of series of natural modes of uncoupled vibrations of free beam. The Ritz method shows very fast convergence and high accuracy. Beside natural frequencies and natural modes, modal stiffness and modal mass are also determined. Application of the developed procedures is illustrated for the case of an elastic barge. In addition, barge vibrations are analysed also by the finite element method utilizing beam model. The intention is to check the reliability of 1D FEM model in hydroelastic analysis of large container ships, where structural model is coupled with 3D hydrodynamic model based on the radiation–diffraction theory.