The coordinate ascent hierarchical infinite element method for the three-dimensional free flexural vibration analysis of water-column interaction systems

Abstract

A simple and highly accurate numerical method is presented for the free flexural vibration analysis of water-column interaction systems. The three-dimensional elasticity theory is used to predict accurately local stresses in the flexible circular column. The effects of water compressibility and gravity surface waves are considered. Small amplitude free vibrations are assumed. A hierarchical finite element is developed to describe the displacements. A coordinate ascent hierarchical infinite element based on the wave equation is developed to describe the hydrodynamic pressure. The method is illustrated with the example of a tapered cantilever circular column. Examples of stepped and parabolic cantilever circular columns are also shown. The method is validated through convergence study and comparison with analytical results for a prismatic cantilever circular column in full contact with water. The cycle frequencies predicted by the Euler-Bernoulli beam theory show deviation from the three-dimensional solutions. New results for the cycle frequencies of tapered, single-stepped, and parabolic cantilever circular columns in full contact with water are provided, which may serve as a benchmark for future research. A parametric study is performed showing the effect of the taper ratio on the cycle frequencies, modal deflections, modal bending stresses, and modal hydrodynamic pressures.