The IUT AM / IFToMM Symposium on Synthesis of Nonlinear Dynamical Systems, held in Riga, Latvia, 24-28 August 1998, was one of a series of IUTAM sponsored symposia which focus on the theory and application of methods of nonlinear dynamics in mechanics. The symposium follows eighteen symposia on Analysis and Synthesis of Nonlinear Mechanical Oscillatory Systems held at Riga Technical University from 1971 to 1991 and in 1996 (prof. E. Lavendelis and Prof. M. Zakrzhevsky). Early in the late fifties and sixties Prof. J. G. Panovko organised several successful conferences in Riga on Nonlinear Oscillations. The participants in all these conferences and symposia (except 1996) were only from the ex-Soviet Union. This symposium, organised by the Institute of Mechanics of Riga Technical University, brought together scientists active in different fields of nonlinear dynamics. Selected scientists from 14 countries represented a wide range of expertise in' mechanics, from pure theoreticians to people primarily oriented towards application of nonlinear and chaotic dynamics and nonlinear oscillations. The goal of the symposium was to stimulate development of the theory of strongly nonlinear dynamical systems and its new applications in the fields of applied mechanics, engineering and other branches of science and technology.

This Volume constitutes the Proceedings of the IUTAM Symposium on 'Scaling Laws in Ice Mechanics and Ice Dynamics', held in Fairbanks, Alaska from 13th to 16th of June 2000. Ice mechanics deals with essentially intact ice: in this discipline, descriptions of the motion and deformation of Arctic/ Antarctic and river/lake ice call for the development of physically based constitutive and fracture models over an enormous range in scale: 0.01 m - 10 km. Ice dynamics, on the other hand, deals with the movement of broken ice: descriptions of an aggregate of ice floes call for accurate modeling of momentum transfer through the sea/ice system, again over an enormous range in scale: 1 km (floe scale) - 500 km (basin scale). For ice mechanics, the emphasis on lab-scale (0.01 - 0.5 m) research con trasts with applications at the scale of order 1 km (ice-structure interaction, icebreaking); many important upscaling questions remain to be explored.

The purpose of this monograph is to show how a compliant offshore structure in an ocean environment can be modeled in two and three di mensions. The monograph is divided into five parts. Chapter 1 provides the engineering motivation for this work, that is, offshore structures. These are very complex structures used for a variety of applications. It is possible to use beam models to initially study their dynamics. Chapter 2 is a review of variational methods, and thus includes the topics: princi ple of virtual work, D'Alembert's principle, Lagrange's equation, Hamil ton's principle, and the extended Hamilton's principle. These methods are used to derive the equations of motion throughout this monograph. Chapter 3 is a review of existing transverse beam models. They are the Euler-Bernoulli, Rayleigh, shear and Timoshenko models. The equa tions of motion are derived and solved analytically using the extended Hamilton's principle, as outlined in Chapter 2. For engineering purposes, the natural frequencies of the beam models are presented graphically as functions of normalized wave number and geometrical and physical pa rameters. Beam models are useful as representations of complex struc tures. In Chapter 4, a fluid force that is representative of those that act on offshore structures is formulated. The environmental load due to ocean current and random waves is obtained using Morison's equa tion. The random waves are formulated using the Pierson-Moskowitz spectrum with the Airy linear wave theory.

Nonlinearity and stochastic structural dynamics is of common interest to engineers and applied scientists belonging to many disciplines. Recent research in this area has been concentrated on the response and stability of nonlinear mechanical and structural systems subjected to random escitation. Simultaneously the focus of research has also been directed towards understanding intrinsic nonlinear phenomena like bifurcation and chaos in deterministic systems. These problems demand a high degree of sophistication in the analytical and numerical approaches. At the same time they arise from considerations of nonlinear system response to turbulence, earthquacke, wind, wave and guidancy excitations. The topic thus attracts votaries of both analytical rigour and practical applications. This books gives important and latest developments in the field presenting in a coherent fashion the research findings of leading international groups working in the area of nonlinear random vibration and chaos.

The interest of the applied mechanics community in chaotic dynamics of engineering systems has exploded in the last fifteen years, although research activity on nonlinear dynamical problems in mechanics started well before the end of the Eighties. It developed first within the general context of the classical theory of nonlinear oscillations, or nonlinear vibrations, and of the relevant engineering applications. This was an extremely fertile field in terms of formulation of mechanical and mathematical models, of development of powerful analytical techniques, and of understanding of a number of basic nonlinear phenomena. At about the same time, meaningful theoretical results highlighting new solution methods and new or complex phenomena in the dynamics of deterministic systems were obtained within dynamical systems theory by means of sophisticated geometrical and computational techniques. In recent years, careful experimental studies have been made to establish the actual occurrence and observability of the predicted dynamic phenomena, as it is vitally needed in all engineering fields. Complex dynamics have been shown to characterize the behaviour of a great number of nonlinear mechanical systems, ranging from aerospace engineering applications to naval applications, mechanical engineering, structural engineering, robotics and biomechanics, and other areas. The International Union of Theoretical and Applied Mechanics grasped the importance of such complex phenomena in the Eighties, when the first IUTAM Symposium devoted to the general topic of nonlinear and chaotic dynamics in applied mechanics and engineering was held in Stuttgart (1989).

This volume contains the papers presented at the IUT AM Symposium of "Mesoscopic Dynamics of Fracture Process and Materials Strength", held in July 2003, at the Hotel Osaka Sun Palace, Osaka, Japan. The Symposium was proposed in 2001, aiming at organizing concentrated discussions on current understanding of fracture process and inhomogeneous deformation governing the materials strength with emphasis on the mesoscopic dynamics associated with evolutional mechanical behaviour under micro/macro mutual interaction. The decision of the General Assembly of International Union of Theoretical and Applied Mechanics (IUT AM) to accept our proposal was well-timed and attracted attention. Driven by the development of new theoretical and computational techniques, various novel challenges to investigate the mesoscopic dynamics have been actively done recently, including large-scaled 3D atomistic simulations, discrete dislocation dynamics and other micro/mesoscopic computational analyses. The Symposium attracted sixty-six participants from eight countries, and forty two papers were presented. The presentations comprised a wide variety of fundamental subjects of physics, mechanical models, computational strategies as well as engineering applications. Among the subjects, discussed are (a) dislocation patterning, (b) crystal plasticity, (c) characteristic fracture of amorphous/nanocrystal, (d) nano-indentation, (e) ductile-brittle transition, (f) ab-initio calculation, (g) computational methodology for multi-scale analysis and others.

The goals ofthe Symposium were to highlight advances in modelling ofatmosphere and ocean dynamics, to provide a forum where atmosphere and ocean scientists could present their latest research results and learn ofprogress and promising ideas in these allied disciplines; to facilitate interaction between theory and applications in atmosphere/ocean dynamics. These goals were seen to be especially important in view ofcurrent efforts to model climate requiring models which include interaction between atmosphere, ocean and land influences. Participants were delighted with the diversity ofthe scientific programme; the opportunity to meet fellow scientists from the other discipline (either atmosphere or ocean) with whom they do not normally interact through their own discipline; the opportunity to meet scientists from many countries other than their own; the opportunity to hear significant presentations (50 minutes) from the keynote speakers on a range ofrelevant topics. Certainly the goal ofcreating a forum for exchange between atmosphere and ocean scientists who need to input to create realistic models for climate prediction was achieved by the Symposium and this goal will hopefully be further advanced by the publication ofthese Proceedings.