Free vibration analysis of a variable cross-section column partially immersed in a liquid

For investigating the dynamic behaviour of the structure under consideration, the effect of the translational and rotational elastic supports, the rotary inertia of the concentrated mass and its eccentricity are all taken into account. The analysis of free vibration frequencies and eigenfunctions of the model, presented in this paper, enables one to obtain very accurate results. The roots of the transcendental frequency equations are obtained by means of the improved conventional analytical (closed-form) solution. The non-dimensional frequency coefficients are given in tabular form. Some numerical examples are presented and the influence of different non-dimensional parameters on frequency values is discussed.