Undamped eigenperiods of a sea-based gravity monotower

An analytically approximate method was proposed in [1] to estimate undamped eigenperiods of a sea-based gravity monotower by accounting for sloshing inside the shaft. These results are generalised to include the soil feedback and the inertia moment of the top rigid body as well as to describe the external hydrodynamic loads using the linear three-dimensional potential flow theory of an incompressible liquid. A mathematical model of the multicomponent mechanical system is presented. The virtual work principle is used to express the Euler-Bernoulli governing equation and all fluid-structure dynamic transmission conditions. Numerical examples of the eigenperiods versus geometric and physical input parameters typical for the Draugen platform and some monopiles are given. The highest eigenperiod of the horizontal vibrations belongs to experimentally-known ranges. These eigenperiods increase with increasing mass, radius of gyration and mass centre of the top body; they also increase with the shear modulus of the soil. Three classes of eigenmodes are detected. They express dominant character of structural vibrations and sloshing, respectively, or a mixed type. Sloshing is less important for existing monopiles.