Multihull vessel excitations in stochastic formulation

Agnieszka Królicka

doi:10.2478/v10012-007-0091-0

Abstract

Multihull vessel excitations in stochastic formulation The article analyses excitations of a multihull vessel using stochastic formulation. The excitations which make the vessel move come from the motion of sea waves and the action of wind. The sea undulation has most frequently the form of irregular waves, and that is why it is assumed in many studies of sea-going vessel dynamics that the undulation process has probabilistic nature. In the article the dynamics of a multihull vessel is analysed using a linear model on which an irregular wave acts. It was assumed that the examined object interacts with the head sea, and for this wave a set of state equations was derived. The head sea provokes symmetric movements of the object, i.e. surge, heave and pitch.

Highlights

The motion of a vessel is mainly provoked by the excitations coming from sea waves
The nature of the wind undulation, along with difficulties in determining precisely the initial conditions for the motion of sea waves, are the reasons why the dynamics of the sea waves can be only modelled within the framework of the stochastic theory [6,7]
The function η(x, y, t) is a random function of time and position [1]. Probabilistic properties of this function are partially derived based on the results of measurements and partially from the hydrodynamic theory of waves. It is usually assumed in dynamic analyses that the process of sea undulation is stationary, ergodic, and Gaussian [8]

Summary

INTRODUCTION

The motion of a vessel is mainly provoked by the excitations coming from sea waves. The nature of the wind undulation, along with difficulties in determining precisely the initial conditions for the motion of sea waves, are the reasons why the dynamics of the sea waves can be only modelled within the framework of the stochastic theory [6,7]. Probabilistic properties of this function are partially derived based on the results of measurements and partially from the hydrodynamic theory of waves It is usually assumed in dynamic analyses that the process of sea undulation is stationary, ergodic, and Gaussian [8]. These assumptions facilitate developing mathematical models, and their effect can be assessed via identification and estimation. For the vessel treated as a rigid object moving at constant speed v and arbitrary angle with respect to the direction of sea waves, its movements can be described by the mathematical model having the form a set of second-order differential equations (1). – vector of exciting forces and moments, can be analysed as a set of two uncoupled groups of mutually coupled equations. Using relevant linear filters we replace the “white noise” process, for which the spectral density is constant, with the densities corresponding to different wave spectra

Deriving the set of state equations

CONCLUSIONS