Spectral Response of Stationary Jack-Up Platforms Loaded by Sea Waves and Wind using Perturbation Method

Abstract

The paper addresses non-linear vibrations of offshore jack-up drilling platforms loaded by sea waves and wind in their stationary condition using the perturbation method. Non-linearity of dynamic equations of motion for fixed offshore platforms yields from two factors. The first is load excitation generating non-linear velocity coupling in a dynamic system. This coupling is inherent in the modified Morison equation, involving the excitation function in the form of the sum of the inertial and velocity forces of sea waves, taking into account relative wave–structure kinematics. Moreover, the wind acting on the exciting side causes similar effects. The second source is the subsoil‒structure interaction problem, modelled by a system of springs and dashpots that yields stochastic non-linearity of the dynamic system. The matrix equations of structural motion in FEM terms are set up. The perturbation method is adopted to determine the mechanical response of the system, making it possible to determine response spectra of the first and the second approximations for displacements and internal forces of the platform. The paper is the continuation of research detailed in the paper [1]. It is assumed, that the fluctuation parts of the dynamic loading forces are in line with the direction of sea wave propagation. Sea current and lift forces effects are neglected in this study. A numerical example refers to structural data of the Baltic drilling platform in the stationary configuration, i.e. when three legs support the deck above the seawater level.