Response statistics of ocean structures to non-linear hydrodynamic loading

Abstract

Abstract This paper presents an analytical approach based on the stochastic averaging of the energy envelope to treat the dynamic behavior of single-degree-of-freedom elastic ocean structures. Such systems are usually subjected to a narrow-band random process which may be modelled as the output of a shaping filter. The response co-ordinates of the system and filter experience slow and fast variations with respect to time, respectively. For this class of problems, the method of stochastic averaging is used to establish stochastic Ito differential equations for the process of slow variation. This approach has not previously been used for non-linear mechanical problems. Three different shaping filters (including those possessing a Pierson-Moskowitz spectrum) are employed to model Gaussian random sea waves. The response statistics of the structure are estimated in terms of the excitation spectrum for different levels of non-linear hydrodynamic drag force. It is found that the hydrodynamic drag reduces the system response energy and consequently suppresses the motion of the structure. In addition, the response probability density deviates from normality as the non-linear hydrodynamic drag parameter increases. The case of non-Gaussian random sea waves will be considered in Part II.