Natural frequencies of an immersed Rayleigh beam carrying an eccentric tip mass with mass moment of inertia

The present paper deals with a method for studying the dynamic analysis of an offshore structure having the form of a column partially immersed in a fluid. The non-uniform column carries a concentrated mass with eccentricity “e” and rotary inertia JM, at its free end. The column is idealized as a Rayleigh beam supported by translational and rotational springs, at the bottom. For investigating the dynamic behaviour of the structure under consideration, the effect of the rotary inertia of the concentrated mass and its eccentricity are all taken into account. Applying theHamilton principle, the equation of motion is derived by means ofa set the orthogonal polynomials, which satisfy the boundary conditions. Taking into account the effects of the kinematic and inertial parameters of the structure, the roots of the transcendental equation are obtained by employing a symbolic numerical code. For analysing the influence of the several non dimensional parameters on natural frequencies values and shape modes, a lot of numerical examples are presented and the results are validated by making comparisons with the results in literature and reported in bibliography.