AVERAGED DAMPING IN RANDOM VIBRATIONS OF THE BALTIC DRILLING PLATFORM

Some findings of an investigation into the stochastic and dynamic response of steel jack-up platforms under wave excitation are discussed. Since the submerged elements of these structures are usually sufficiently slender, one can use a modified Morison equation for evaluation of the in-line component of wave force. Transverse forces and the influence of vortex shedding are ignored in this study. The modified form of the Morison equation under the relative velocity assumption contains a non-linear function of the Gaussian wave particle kinematics and a non-linear term in the structural response velocity. The mathematical considerations of the problem formulated are based on the stochastic averaging method. The response is approximated by a diffusive Markov vector process analyzed by using Itô's stochastic differential equations. From the stationary solution of these equations, statistics of second order are derived. The stability conditions or stochastic averaging used for the dissipative energy of the vibrating system gives an expression for the equivalent damping ratio. Illustrative analyses of a one-degree-of-freedom system and a numerical example referred to engineering problems of a Baltic drilling platform are presented. The sea surface is described by the one-dimensional wave spectrum proposed by Striekalov and Massel for the Baltic Sea. © 1990.