By I. I. Blekhman (auth.), E. Lavendelis, M. Zakrzhevsky (eds.)

The IUT AM / IFToMM Symposium on Synthesis of Nonlinear Dynamical structures, held in Riga, Latvia, 24-28 August 1998, used to be one in every of a sequence of IUTAM backed symposia which specialise in the speculation and alertness of tools of nonlinear dynamics in mechanics. The symposium follows eighteen symposia on research and Synthesis of Nonlinear Mechanical Oscillatory structures held at Riga Technical college from 1971 to 1991 and in 1996 (prof. E. Lavendelis and Prof. M. Zakrzhevsky). Early within the overdue fifties and sixties Prof. J. G. Panovko organised numerous winning meetings in Riga on Nonlinear Oscillations. The members in a lot of these meetings and symposia (except 1996) have been purely from the ex-Soviet Union. This symposium, organised via the Institute of Mechanics of Riga Technical collage, introduced jointly scientists lively in several fields of nonlinear dynamics. chosen scientists from 14 nations represented a variety of services in' mechanics, from natural theoreticians to humans basically orientated in the direction of program of nonlinear and chaotic dynamics and nonlinear oscillations. The objective of the symposium was once to stimulate improvement of the idea of strongly nonlinear dynamical platforms and its new purposes within the fields of utilized mechanics, engineering and different branches of technological know-how and technology.

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Subsequently, again stable quasi-periodic behaviour was found which locks to 22 VAN CAMPEN ET AL. 1/2 subharmonic behaviour in the frequency range w :::::: 675 - 690 rad/s with substantial values of IZmlmax (see inset in figure 5). After this frequency range the stable quasi-periodic behaviour recovers until in the frequency range w :::::: 950 - 1020 rad/s the harmonic solution becomes stable again. Finally, for w > 1020 rad/s again stable quasi-periodic behaviour was found. The dotted line in figure 5 represents the dynamic response of the model if the equations of motion are linearized with respect to the" static" solution occurring for me = 0 g.

Institut fUr Schiffbau der Universitiit Hamburg, Bericht Nr. 512, Hamburg. , WENDT, M. (1998) Stabilitiit von Schiffsbewegungen, Z. Angew. Math. , to appear. LLOYD A. R. J. M. (1989) Seakeeping: Ship Behaviour in Rough Weather. Ellis Horwood Limited, Chichester, England. PEREIRA, R. (1997) Simulation nichtlinearer Seegangslasten, Schiffstechnik 35, pp. 173193 PETEY F. (1988) Ermittlung der Kentersicherheit lecker Schiffe im Seegang, Schiffstechnik, 35, pp. 155-172. , STAVETSKI, D. (1993) SPLASH Free-Surface Flow Code Methodology for Hydrodynamic Design and Analysis of IACC Yachts, The Eleventh Chesapeake Sailing Yacht Symposium, Annapolis, MD, 35, pp.

The free surface is not discretized. Consequently, Green's functions that implicit ely fulfill the boundary conditions at the free surface have to be used. 1. This is done for many different heelings and drafts of the ship and for all frequencies of interest, (Pereira, 1988). The frequency dependent coefficients are transformed to the time domain in order to be able to perform time domain simulation. An approximate inverse Laplace transformation is used and yields a linear system of state equations (state model) with constant coefficients depending on the heeling, draft, and cross-section.