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

The IUT AM / IFToMM Symposium on Synthesis of Nonlinear Dynamical platforms, held in Riga, Latvia, 24-28 August 1998, used to be one among a chain of IUTAM backed symposia which concentrate on the idea and alertness of tools of nonlinear dynamics in mechanics. The symposium follows eighteen symposia on research and Synthesis of Nonlinear Mechanical Oscillatory platforms held at Riga Technical college from 1971 to 1991 and in 1996 (prof. E. Lavendelis and Prof. M. Zakrzhevsky). Early within the past due fifties and sixties Prof. J. G. Panovko organised numerous profitable meetings in Riga on Nonlinear Oscillations. The contributors in some of these meetings and symposia (except 1996) have been basically from the ex-Soviet Union. This symposium, organised via the Institute of Mechanics of Riga Technical college, 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 aim of the symposium was once to stimulate improvement of the speculation of strongly nonlinear dynamical platforms and its new functions within the fields of utilized mechanics, engineering and different branches of technology and technology.

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**Sample text**

They depend on the actual heeling and draft. For large roll, heave, and pitch motions it is therefore necessary to switch between the coefficients. Finally, all the strips are joined together by compatible boundary conditions and the forces for the complete system are integrated along the ship length. The diffraction forces are not calculated using the diffraction potential but implicit ely with the radiation forces using the so-called concept of relative velocities. Instead of using the absolute velocity in the state model, the relative velocity between the strip and the surrounding water is inserted.

2. RESULTS Figure 5 shows the maximum absolute displacements IZm Imax (over one period of the solution) as function of the angular rotor speed w. For angular rotor speeds w not exceeding about 600 rad/s only so-called harmonic solutions are found with the same period time as that of the angular shaft rotation. 038 m, m. = 1 9 1z",1.... 00E-5 o 250 500 750 1000 OJ [radls] Figure 5. 0 g. secondary Hopf bifurcation. In the subsequent small frequency range of unstable harmonic solutions stable quasi-periodic behaviour was found until the harmonic solution becomes stable again via a second secondary Hopf bifurcation.

Hydrodynamic Approach In SIMBEL the ship is represented by a number of cross-sections - transverse, finite strips into which the hull is imagined to be cut. For each strip the local hydrodynamic properties are determined. Later, the strips are all joined together by compatible boundary conditions and the coefficients for the complete system are integrated. It is assumed that the ship is slender, the hull is rigid, the speed is moderate, the motions are small, and the water is deep. Then, it can be assumed that the local hydrodynamic properties are the same as would be experienced if the strip were part of an infinitely long cylinder of the same cross-sectional shape as shown in Fig.