Free transverse vibration of mono-piled ocean tower

The free vibration of a continuous, elastic model of a mono-piled ocean tower is studied. The tower, partially submerged in water, is undergoing free transverse vibration in a plane. It is modeled as a non-uniform Timoshenko beam which has an eccentric tip mass on one end and is supported by a mono-piled foundation on the other. Effects of shear deformation and rotary inertia are included in the beam. The problem of interaction of soil with the pile is solved by adopting the Winkler Foundation model. The viscoelastic character of the soil is included using the Kelvin-Voigt model. Equation of motion of the tower is derived using Hamilton׳s variational principle and approximate analytical solution is found using the Rayleigh Ritz Method (RRM). The solution is compared with that obtained from a conventional Finite Element Method (FEM) which shows a good agreement. The trial function of RRM is assumed as uniform beam mode-shapes satisfying the boundary and continuity conditions of the ocean tower. At the end, an extensive parametric study is carried out which provides an insight into the dependence of natural frequency on different configurations of the tower.