Abstract
State equations in the mathematical model of dynamic behaviour of multihull floating unit This paper concerns dynamic behaviour of multihull floating unit of catamaran type exposed to excitations due to irregular sea waves. Dynamic analysis of multihull floating unit necessitates, in its initial stage, to determine physical model of the unit and next to assume an identified mathematical model. Correctly elaborated physical models should contain information on the basis of which a mathematical model could be built. Mathematical models describe mutual relations between crucial quantities which characterize a given system in time domain. The dynamic analysis of multihull unit was performed under assumption that the unit's model has been linear and exposed to action of irregular sea waves. Mathematical model of such dynamic system is represented by state equations. The formulated equations take into account encounter of head wave which generates symmetrical motions of the unit, i.e. surge, heave and pitch. For solving the equations the following three wave spectra were taken into consideration: - ISSC (International Ship Structures Congress) spectrum - Pierson-Moskowitz spectrum - Paszkiewicz spectrum.
Highlights
Motion of a dynamic system can be generated by diferent external or internal factors.At mathematical modelling external excitation factors of the most significant effect on the system, are selected
For a broad class of dynamic systems the relation between excitations and response is characterized by differential equations of motion.The equations can be linear or non-linea,r of constant or varying coefficients, ordinary or dif ferential, deterministic or stochastic ones
The wave height processes are generated by the transfer mathematical model of a dynamic system.An alternative way function G(s) which constitutes the so-called shape filter to describe a dynamic system is transmittance in which the if „white noise” is at input
Summary
Motion of a dynamic system can be generated by diferent external or internal factors.At mathematical modelling external excitation factors of the most significant effect on the system, are selected. For a broad class of dynamic systems the relation between excitations and response is characterized by differential equations of motion.The equations can be linear or non-linea,r of constant or varying coefficients, ordinary or dif ferential, deterministic or stochastic ones. State variables and input parameters of the models are of probabilistic character Mathematical models of such systems are represented by sets of stochastic dif ferential equations, and form sets of Itô Itequations. Multihull units such as catamarans and trimarans belong to complex, highly non-linear dynamic systems. Constructional reasons (symmetry) of multihull floating units make it possible to analyze group-coupled motions of the object and in consequence to limit number of state variables which appear in the equations
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