On the natural frequencies of variable cross-section Timoshenko beam with concentrated tip mass immersed in a fluid

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. In the present modeling method, the shear and the rotary inertia effects on the modal characteristics are correctly included based on the Timoshenko beam theory. The potential and kinetic energy expression of this model are derived from the Rayleigh-Ritz method, using a set of function polynomial . The equation thus derived are transmitted into dimensionless forms in which main dimensionless parameters are identified. The effects of the dimensionless parameters such as the slenderness ration, tip mass, etc. on the natural frequencies and modal characteristics of immersed beam are successfully examined trough numerical studies. Results of the present study are compared with some analytical solutions in references