At the end of the twentieth century, nonlinear dynamics turned out to be one of the most challenging and stimulating ideas. Notions like bifurcations, attractors, chaos, fractals, etc. have proved to be useful in explaining the world around us, be it natural or artificial. However, much of our everyday understanding is still based on linearity, i. e. on the additivity and the proportionality. The larger the excitation, the larger the response-this seems to be carved in a stone tablet. The real world is not always reacting this way and the additivity is simply lost. The most convenient way to describe such a phenomenon is to use a mathematical term-nonlinearity. The importance of this notion, i. e. the importance of being nonlinear is nowadays more and more accepted not only by the scientific community but also globally. The recent success of nonlinear dynamics is heavily biased towards temporal characterization widely using nonlinear ordinary differential equations. Nonlinear spatio-temporal processes, i. e. nonlinear waves are seemingly much more complicated because they are described by nonlinear partial differential equations. The richness of the world may lead in this case to coherent structures like solitons, kinks, breathers, etc. which have been studied in detail. Their chaotic counterparts, however, are not so explicitly analysed yet. The wavebearing physical systems cover a wide range of phenomena involving physics, solid mechanics, hydrodynamics, biological structures, chemistry, etc.

This book collects invited lectures presented and discussed on the AMAS & ECCOMAS Workshop/Thematic Conference SMART'o3. The SMART'o3 Conference on Smart Materials and Structures was held in a 19th century palace in Jadwisin near Warsaw, 2-5 September 2003, Poland .It was organized by the Advanced Materials and Structures (AMAS) Centre of Excellence at the Institute of Fundamental Technological Research (IFTR) in Warsaw, ECCOMAS - European Community on Computational Methods in Applied Sciences and SMART-TECH Centre at IFTR. The idea of the workshop was to bring together and consolidate the community of Smart Materials and Structures in Europe. The workshop was attended by 66 participants from n European countries (Austria, Belgium, Finland, France, Germany, Italy, Poland, Portugal, Spain, U.K., Ukraine), 1 participant from Israel and 1 participant from the USA. The workshop program was grouped into the following major topics: 4 sessions on Structural Control (18 presentations), 3 sessions on Vibration Controland Dynamics (14 presentations), 2 sessions on Damage Identification (10 presentations), 2 sessions on Smart Materials (9 presentations). Each session was composed of an invited lecture and some contributed papers. Every paper scheduled in the program was presented, so altogether 51 presentations were given. No sessions were run in parallel. The workshop was attended not only by researchers but also by people closely related to the industry. There were interesting discussions on scientific merits of the presented papers as well as on future development of the field and its possible industrial applications.

We are honoured to present this collection of selected papers from the International Conference on Mixing and Crystallization, held at the Tioman Island, Malaysia in April, 1998. We are grateful to the editorial board comprising five eminent researchers in the field of mixing and crystallization for their thoughtful review and suggestions. In order to make this book as current as possible some of the papers have been thoroughly revised, which caused some delay in bringing out this edited version. We received necessary support from the Institute of Post Graduate Studies and Research, the University of Malaya and the Special Research Centre for Multiphase Processes, and the University of Newcastle, Australia in organizing this conference. We are indebted to the Institute of Chemical Engineers, United Kingdom, and the Institution of Engineers, Malaysia for their sponsorship. We would like to thank K.C. Lim, Dr. C. Ramakanth and Ms. Zubaidah for their help at the various stages of editing. We would also like to express our gratitude to Professor Mohd. Ali Hashim and Dr. Nafis Ahmed for their help and encouragement. Finally, I would like to thank Kluwer Academic Publishers for publishing this book. Bhaskar Sen Gupta Shaliza Ibrahim University of Malaya, Kuala Lumpur xi CFD MODELLING OF HYDRODYNAMIC CONDITIONS WITHIN THE WAKE OF MIXING IMPELLER BLADES 1 G.D. RIGByl., G. LANE . AND G.M. EVANSl.

In determining the response of offshore structures, it is of utmost importance to determine, in the most correct manner, all factors which contribute to the total force acting on these structures. Applying the Morison formula (Morison et. al. , 1950) to calculate forces on offshore slender structures, uncertainties related to the understanding of the wave climate, the hydrodynamic force coefficients and the kinematics of ocean waves represent the most important contributions to the uncertainties in the prediction of the total forces on these structures (Haver and Gudmestad, 1992). Traditional calculation of forces on offshore structures involves the use of regular waves with the following non-linearities inco1porated use of regular wave theories inco1porating higher order terms use of Morison equation having a nonlinear drag term inclusion of the effect of the free surface by integrating all contributions to total forces and moments from the sea floor to the free surface of the waves In order to describe the sea more realistically, the ocean surface is to be described as an irregular sea surface represented by its energy spectrum. The associated decomposition of the sea surface is given as a linear sum of linear waves. The total force is found by integrating the contribution from all components in the wave spectrum to the free surface. The kinematics of each component must therefore be determined.

This monograph presents an updated source of information on the state of the art in advanced control of articulated and mobile robots. It includes relevant selected problems dealing with enhanced actuation, motion planning and control functions for articulated robots, as well as of sensory and autonomous decision capabilities for mobile robots. The basic idea behind the book is to provide a larger community of robotic researchers and developers with a reliable source of information and innovative applications in the field of control of cooperating and mobile robots. This book is the outcome of the research project MISTRAL (Methodologies and Integration of Subsystems and Technologies for Anthropic Robotics and Locomotion) funded in 2001-2002 by the Italian Ministry for Education, University and Research. The thorough discussion, rigorous treatment, and wide span of the presented work reveal the significant advances in the theoretical foundation and technology basis of the robotics field worldwide.

Acoustical imaging has become an indispensable tool in a variety of fields. Since its introduction, the applications have grown and cover a variety of techniques, producing significant results in fields as disparate as medicine and seismology. Cutting-edge trends continue to be discussed worldwide.

This book contains the proceedings of the 27th International Symposium on Acoustical Imaging (AI27), which took place in Saarbrucken, Germany, from March 24th to March 27th 2003. The Symposium belongs to a conference series in existence since 1968. AI27 comprised sessions on:

• Medical Imaging,
• Non-Destructive Testing,
• Seismic Imaging,
• Physics and Mathematics of Acoustical Imaging,
• Acoustic Microscopy.

During two well-attended workshops the applications of quantitative acoustical imaging in biology and medical applications, and in near-field imaging of materials, were discussed. Based on its cross-disciplinary aspects, the authors of the papers of AI27 present experiments, theory and construction of new instruments.

Audience: This volume will be of interest to engineers and researchers of all levels in the field, in industry or academia, and for those newcomers who want to get acquainted with the state-of-the-art in acoustical imaging. "

The survival of the Aeronautical Industries of Europe in the highly competitive World Aviation Market is strongly dependent on such factors as time-to-market of a new or derivative aircraft and on its manufacturing costs but also on the achievement of a competitive technological advantage by which an increased market share can be gained. Recognizing this, cooperative research is continuously encouraged and co-financed by the European Union in order to strengthen the scientific and technological base of the Aeronautical Industries thus providing - among others - the technological edge needed for survival. Corresponding targets of research within Area 3, Technologies for Transport Means, and here in particular Area 3A, Aeronautics Technologies, of the Industrial and Materials Technologies Program ( Brite -EuRam III, 1994 -1998) have been identified to be aircraft efficiency, cost effectiveness and environmental impact. Concerning aircraft efficiency - relevant to the present research - a reduction in aircraft drag of 10%, a reduction in aircraft fuel consumption of 30%, and a reduction in airframe, engine and system weight of 20% are envisaged. Meeting these objectives has, of course, also a strong positive impact on the environment.

Undeservedly little attention is paid in the vast literature on the theories of vibration and plasticity to the problem of steady-state vibrations in elastoplastic bodies. This problem, however, is of considerable interest and has many important applications. The problem of low-cyclic fatigue of metals, which is now in a well de veloped state is one such application. The investigations within this area are actually directed to collecting experimental facts about repeated cyclic loadings, cf. 47J. Theoretical investigations within this area usually con sider the hysteretic loops and the construction of models of plasticity theory which are applicable to the analysis of repeated loadings and the study of the simplest dynamic problems. Another area of application of the theory of the vibration of elastoplas tic bodies is the applied theory of amplitude-dependent internal damping. Another name for this theory is the theory of energy dissipation in vibrat ing bodies. In accordance with the point of view of Davidenkov "internal damping" in many metals, alloys and structural materials under consider able stress presents exactly the effect of micro plastic deformations. There fore, it may be described by the methods of plasticity theory. This point of view is no doubt fruitful for the theory of energy dissipation in vibrating bodies, as it allows one to write down the constitutive equations appropri ate both for vibrational analysis of three-dimensional stress states and an investigation of nonharmonic deformation. These problems are known to be important for the theory of internal damping."

Asymptotic methods of nonlinear mechanics developed by N. M. Krylov and N. N. Bogoliubov originated new trend in perturbation theory. They pene- trated deep into various applied branches (theoretical physics, mechanics, ap- plied astronomy, dynamics of space flights, and others) and laid the founda- tion for lrumerous generalizations and for the creation of various modifications of thesem. E!f,hods. A great number of approaches and techniques exist and many differen. t classes of mathematical objects have been considered (ordinary differential equations, partial differential equations, delay diffe,'ential equations and others). The stat. e of studying related problems was described in mono- graphs and original papers of Krylov N. M. , Bogoliubov N. N. [1], [2], Bogoli- ubov N. N [1J, Bogoliubov N. N. , Mitropolsky Yu. A. [1], Bogoliubov N. N. , Mitropol- sky Yu. A. , Samoilenko A. M. [1], Akulenko L. D. [1], van den Broek B. [1], van den Broek B. , Verhulst F. [1], Chernousko F. L. , Akulenko L. D. and Sokolov B. N. [1], Eckhause W. [l], Filatov A. N. [2], Filatov A. N. , Shershkov V. V. [1], Gi- acaglia G. E. O. [1], Grassman J. [1], Grebennikov E. A. [1], Grebennikov E. A. , Mitropolsky Yu. A. [1], Grebennikov E. A. , Ryabov Yu. A. [1], Hale J . K. [I]' Ha- paev N. N. [1], Landa P. S. [1), Lomov S. A. [1], Lopatin A. K. [22]-[24], Lykova O. B.

Results of experimental research on aerodynamic and acoustic control of subsonic turbulent jets by acoustic excitation are presented. It was demonstrated that these control methods, originated by authors, not only can intensify mixing (by acoustic irradiation at low frequency), but also notably ease it (at high-frequency irradiation). This research monograph presents the updated results of the authors supplemented by other investigations conducted in USA, Germany and Great Britain. The methods for the numerical simulation of subsonic turbulent jets under acoustic excitation are described in detail, and examples are reviewed of practical applications, including reduction of turbojet engine noise and acoustic control of self-sustained oscillations in wind tunnels.

This book has evolved from a course on Mechanics of Robots that the author has thought for over a dozen years at the University of Cassino at Cassino, Italy. It is addressed mainly to graduate students in mechanical engineering although the course has also attracted students in electrical engineering. The purpose of the book consists of presenting robots and robotized systems in such a way that they can be used and designed for industrial and innovative non-industrial applications with no great efforts. The content of the book has been kept at a fairly practical level with the aim to teach how to model, simulate, and operate robotic mechanical systems. The chapters have been written and organized in a way that they can be red even separately, so that they can be used separately for different courses and readers. However, many advanced concepts are briefly explained and their use is empathized with illustrative examples. Therefore, the book is directed not only to students but also to robot users both from practical and theoretical viewpoints. In fact, topics that are treated in the book have been selected as of current interest in the field of Robotics. Some of the material presented is based upon the author's own research in the field since the late 1980's.

This volume is a record of the proceedings of the Symposium on Statistical Energy Analysis (SEA) held at the University of Southampton in July 1997 which was held under the auspices of the International Union of Theoretical and Applied Mechanic . Theoretical SEA is form of modelling the vibrational and acoustical behaviour of complex mechanical systems which has undergone a long period of gestation before recent maturation into a widely used engineering design and analysis tool which is supported by a rapidly growing supply of commercial software. SEA also provides a framework for associated experimental measurement procedures, data analysis and interpretation. Under the guidance of the members of a distinguished International Scientific Committee, participants were individually invited from the broad spectrum of 'SEAfarers', including academics, consultants, industrial engineers, software developers and research students. The Symposium aimed to reflect the balance of world-wide activity in SEA, although some eminent members of the SEA community were, sadly, unable to attend. In particular, Professor Richard Lyon and Dr Gideon Maidanik, two of the principal originators of SEA, were sorely missed. This publication contains copies of all the papers presented to the Symposium together with a summary of the associated discussions which contains valuable comments upon the contents of the formal papers together with the views of participants on some fundamental issues which remain to be resolved.

model. They conclude that the models using three fitting parameters provide the best fit over a wide range of suctions. Models for soil-water characteristic curves are only useful if we have experimental data on which to base them. Agus, Leong and Rahardjo (Singapore) present a large number of experimental soil-water characteristic curves determined for two types of residual soil from Sigapore. They present data for eight different sites. This data set allows them to relate the parameters of the soil-water characteristic curves to index properties. They conclude that the relationships derived are suitable to pro vide a quick preliminary estimate of a soil-water characteristic curve. The importance of soil-water characteristic curves is emphasized by another con tribution dealing with this topic. Aung, Rahardjo, Leong and Toll (Singapore) inves tigate the relationship between mercury intrusion porosimetry measurements and soil-water characteristic curves. The porosimetry measurements are presented as soil-air characteristic curves. The slopes of the soil-air characteristic curves are found to be similar to the slopes of the soil-water characteristic curves. The equiv alent pore diameters calculated from the mercury entry value and the air entry value appear to be related. Therefore, it is suggested that porosimetry data can be used to construct an estimate of the soil-water characteristic curve."

Many dynamical systems are described by differential equations that can be separated into one part, containing linear terms with constant coefficients, and a second part, relatively small compared with the first, containing nonlinear terms. Such a system is said to be weakly nonlinear. The small terms rendering the system nonlinear are referred to as perturbations. A weakly nonlinear system is called quasi-linear and is governed by quasi-linear differential equations. We will be interested in systems that reduce to harmonic oscillators in the absence of perturbations. This book is devoted primarily to applied asymptotic methods in nonlinear oscillations which are associated with the names of N. M. Krylov, N. N. Bogoli ubov and Yu. A. Mitropolskii. The advantages of the present methods are their simplicity, especially for computing higher approximations, and their applicability to a large class of quasi-linear problems. In this book, we confine ourselves basi cally to the scheme proposed by Krylov, Bogoliubov as stated in the monographs 6,211. We use these methods, and also develop and improve them for solving new problems and new classes of nonlinear differential equations. Although these methods have many applications in Mechanics, Physics and Technique, we will illustrate them only with examples which clearly show their strength and which are themselves of great interest. A certain amount of more advanced material has also been included, making the book suitable for a senior elective or a beginning graduate course on nonlinear oscillations."

T his book presents a t.hooretical framewerk and control methodology for a class of complcx dyna.mical systenis characterized by high state space dimension, multiple inpu t.s anrl out puts. significant nonlinearity, parametric uncertainty and unmodellod dyuarni cs. The book start.s wit.h an inl.rod uct.orv Chapter 1 where the peculiari- ties of control problcrns Ior complex systems are discussed and motivating examples from different fiolds of seience and technology are given. Chapter 2 prcscnts SO Il I(' rcsults of nonlinear control theory which assist in reading subsequent chaptors. The main notions and concepts of stability theory are int roduced. and problems of nonlinear transformation of sys- tem coordinates an' discussod. On this basis, we consider different design techniques and approaches t 0 linearization. stabilization and passification of nonlinear dynamical SySt('IIIS. Chapter 3 gives an cx posit.ion of the Speed-Gradient method and its ap- plications to nonlinear aud adaptive control. Convergence and robustness properties are exam iued. I~ roblcms of rcgulat ion, tracking, partial stabiliza- tion and control of 11amiItonia.n systerns are considered .

There has been a growing interest in the foundation of the theory of th- walled composite beams and of their incorporation in aeronautical/aerospace, automotive, helicopter and turbomachinery rotor blades, mechanical, civil and naval constructions inthe last two decades or so. The proliferation of the specialized literature, mainly in the form of journal/ proceedings papers, and the activity in terms of workshops devoted to this topic attest this interest. A decisive factor that has fueled thisgrowing activity was generatedby highdiversity and severity ofdemandsand operating conditions imposed on structural elements involvedintheadvanced technology. In order to beable to survive andful?ll theirmission inthe extreme environmental conditions inwhich they operate, new materialsand new structural paradigms are required. The new exotic structures have to provide higher performances, unatta- able bytheclassical structures builtof traditional materials. Theadvent of advanced composite materials, of smart materialsandfunctionally graded - terials (FGMs), have constituted the strongest stimuli for suchdevelopments. Moreover, their incorporation is likely to expand the use and capabilities of thin-walledbeam structures. Thenew and stringent requirements imposed on aeronautical/aerospace, turbomachinery and shaft structural systems will be best met by such new types of material structures

The contributions in this book were presented at the sixth international symposium on Advances in Robot Kinematics organised in June/July 1998 in Strobl/Salzburg in Austria. The preceding symposia of the series took place in Ljubljana (1988), Linz (1990), Ferrara (1992), Ljubljana (1994), and Piran (1996). Ever since its first event, ARK has attracted the most outstanding authors in the area and managed to create a perfect combination of professionalism and friendly athmosphere. We are glad to observe that, in spite of a strong competition of many international conferences and meetings, ARK is continuing to grow in terms of the number of participants and in terms of its scientific impact. In its ten years, ARK has contributed to develop a remarkable scientific community in the area of robot kinematics. The last four symposia were organised under the patronage of the International Federation for the Theory of Machines and Mechanisms -IFToMM. interest to researchers, doctoral students and teachers, The book is of engineers and mathematicians specialising in kinematics of robots and mechanisms, mathematical modelling, simulation, design, and control of robots. It is divided into sections that were found as the prevalent areas of the contemporary kinematics research. As it can easily be noticed, an important part of the book is dedicated to various aspects of the kinematics of parallel mechanisms that persist to be one of the most attractive areas of research in robot kinematics.

Tensor Analysis and Nonlinear Tensor Functions embraces the basic fields of tensor calculus: tensor algebra, tensor analysis, tensor description of curves and surfaces, tensor integral calculus, the basis of tensor calculus in Riemannian spaces and affinely connected spaces, - which are used in mechanics and electrodynamics of continua, crystallophysics, quantum chemistry etc.

The book suggests a new approach to definition of a tensor in space R3, which allows us to show a geometric representation of a tensor and operations on tensors. Based on this approach, the author gives a mathematically rigorous definition of a tensor as an individual object in arbitrary linear, Riemannian and other spaces for the first time.

It is the first book to present a systematized theory of tensor invariants, a theory of nonlinear anisotropic tensor functions and a theory of indifferent tensors describing the physical properties of continua.

The book will be useful for students and postgraduates of mathematical, mechanical engineering and physical departments of universities and also for investigators and academic scientists working in continuum mechanics, solid physics, general relativity, crystallophysics, quantum chemistry of solids and material science.

This monograph is devoted to nonlinear dynamics of thin plates and shells with thermosensitive excitation. Because of the variety of sizes and types of mathematical models in current use, there is no prospect of solving them analytically. However, the book emphasizes a rigorous mathematical treatment of the obtained differential equations, since it helps efficiently in further developing of various suitable numerical algorithms to solve the stated problems.

There are many monographs in the existing literature devoted to the static and dynamic behavior of plates and shells. Plates and shells are enco- tered often in engineering applications being integralparts of a wide range of constructions, such as machines, vehicles, airplanes, rockets, ships, bridges, buildings, and containers, to name a few. In addition to the usual requi- ments posedby engineersrelatedtolightweightness, su?cientrigidityor?- ibility, and robust stability properties, there is an additional class ofapriori dynamicalpropertiesrequiredbymodernengineeringapplicationswheren- homogeneity and non-uniformity of structural components is often the norm incertainapplications. Inaddition, strictoperationalrequirementsinmodern engineering applications towards higher speeds, lighter construction, robust andreliableperformance, dictatessmallermarginsoferrorordeviationsfrom prescribed performances in adverse or uncertain forcing environments. This, in turn, requires the development of new analytical and computational tools capable of addressing challenging and not very well developed topics, such as, nonlinearities a?ecting the system performance, the e?ects of unmodeled dynamics on the stability of operation, and the role of uncertainties in the systemparametersonthestructuralresponse. Asaresult, thereisanongoing e?ort to address such issues, leading to the development of new analytical and computational tools, some of which are discussed in this monograph. The monograph follows an approach based on an integrated treatment of analysis and computation. Such a hybrid approach, coupled with computer algebra, can lead to results that cannot be obtained by other standard th- ries in the ?eld. We show, that in a wide class of problems only a carefully prepared numerical experiment followed by purely mathematical conside- tionscan?nallyleadtothesoughtresults. Thenumerousanalyticalconstr- tions are illustrated by examples of application and computational resu

The area of analysis and control of mechanical systems using differential geometry is flourishing.

This book collects many results over the last decade and provides a comprehensive introduction to the area.

The ECCOMAS Thematic Conference Multibody Dynamics 2005 was held in Madrid, representing the second edition of a series which began in Lisbon 2003. This book contains the revised and extended versions of selected conference communications, representing the state-of-the-art in the advances on computational multibody models, from the most abstract mathematical developments to practical engineering applications.

Servo Motors and Industrial Control Theory presents the fundamentals of servo motors and control theory in a manner that is accessible to undergraduate students, as well as practitioners who may need updated information on the subject. Graphical methods for classical control theory have been replaced with examples using mathematical software, such as MathCad and MatLab, to solve real-life engineering control problems. State variable feedback control theory, which is generally not introduced until the Masters level, is introduced clearly and simply for students to approach complicated problems and examples.

The International Symposium on History of Machines and Mechanisms is a new initiative to promote explicitly researches and publications in the field of the History of TMM (Theory of Machines and Mechanisms). It was held at the University of Cassino, Italy, from 11 to 13 May 2000. The Symposium was devoted mainly to the technical aspects of historical developments and therefore it has been addressed mainly to the IFToMM Community. In fact, most the authors of the contributed papers are experts in TMM and related topics. This has been, indeed, a challenge: convincing technical experts to go further in-depth into the background of their topics of expertise. We have received a very positive response, as can be seen by the fact that these Proceedings contain contributions by authors from all around the world. We received about 50 papers, and after review about 40 papers were accepted for both presentation and publishing in the Proceedings. This means also that the History of TMM is of interest everywhere and, indeed, an in-depth knowledge of the past can be of great help in working on the present and in shaping the future with new ideas. I believe that a reader will take advantage of the papers in these Proceedings with further satisfaction and motivation for her or his work (historical or not). These papers cover the wide field of the History of Mechanical Engineering and particularly the History of TMM.