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2 Vibrations in Physical Systems

2 2008

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Stochastic approach to movements of a multihull on waves

Królicka A.

Vibrations in Physical Systems

2008

Vol. 23

217--222

Due to difficulties in determining precise initial conditions for the motion of sea waves and the nature of wind undulation, the dynamics of sea waves can be only modelled within the framework of a stochastic theory. The article presents a method for determining differential equations of motion for multihulls, such as catamaran or trimaran. The catamaran sails at constant translatory velocity and at an arbitrary angle to the undulation direction. The set of differential equations of motion presented in the article models anti-symmetric (lateral) movements of the catamaran. For those movements, stochastic differential equations ( Itô equations) are constructed in the form of the equation set (8). Using the state vector X and the excitation vector Y , the Itô equations take the form (9) and (10).

External loads for multihull watercraft

Trębacki K., Królicka A.

Vibrations in Physical Systems

2008

Vol. 23

371--376

For multihull watercraft, general differential equations of motion were formulated taking into account possible movements of the oceanotechnic construction. These movements are connected with freedom degrees of the construction floating on the undulated sea surface. General formulas given for possible construction movements describe the external loads connected with hydrodynamic reactions, damping forces and hydrostatic reactions. The generalised excitation forces can refer to the case of regular undulation and for this case general formulas are given. Irregular sea undulation, which is a stochastic process, requires using linear filters developed based on parametric wave excitations relating to one of spectra collected in Table 1.