Natural frequencies of a immersed Rayleigh-beam carrying a tip mass with rotary inertia

In the present paper, the free vibration analysis of an offshore structure, having the form of a column partially immersed in a liquid, is presented. A beam without contacting with water is called the dry beam, while the one partially immersed in water is called the wet beam. The column is modelled as a Rayleigh beam. For investigating the dynamic behaviour of the structure under consideration, the effect 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 the improved conventional analytical approximate 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