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 December 1994 Professor Enok Palm celebrated his 70th birthday and retired after more than forty years of service at the University of Oslo. In view of his outstanding achievements as teacher and scientist a symposium entitled "Waves and Nonlinear Processes in Hydrodynamics" was held in his honour from the 17th to the 19th November 1994 in the locations of The Norwegian Academy of Science and Letters in Oslo. The topics of the symposium were chosen to cover Enok's broad range of scientific work, interests and accomplishments: Marine hydrodynamics, nonlinear wave theory, nonlinear stability, thermal convection and geophys ical fluid dynamics, starting with Enok's present activity, ending with the field where he began his career. This order was followed in the symposium program. The symposium had two opening lectures. The first looked back on the history of hydrodynamic research at the University of Oslo. The second focused on applications of hydrodynamics in the offshore industry today.

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.

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. "

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."

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.

It is well known that noise control at the source is the most cost-effective. Designing for quietness is therefore the most important concept in Engineering Acoustics or Technical Acoustics. The IUTAM Symposium on Designing for Quietness held at the Indian Institute of Science Bangalore in December 2000, was probably the first on this topic anywhere in the world. Papers were invited from reputed researchers and professionals spread over several countries. 18 of the 21 papers presented in the Symposium are included in these proceedings after rigorous review, revision and editing. This volume covers a large number of applications, such as silencers, lined ducts, acoustic materials, source characterization, acoustical design of vehicle cabs, ships, space antennas, MEMS pressure transducer etc., active control of structure-borne noise and cavities, SEA for engine noise and structural acoustic modelling with application to design of quieter panels.
A list of references at the end of every paper will provide sources for further reading.

In this monograph I record those parts of the theory of transverse isotropic elastic wave propagation which lend themselves to an exact treatment, within the framework of linear theory. Emphasis is placed on transient wave motion problems in two- and three-dimensional unbounded and semibounded solids for which explicit results can be obtained, without resort to approximate methods of integration. The mathematical techniques used, many of which appear here in book form for the first time, will be of interest to applied mathematicians, engeneers and scientists whose specialty includes crystal acoustics, crystal optics, magnetogasdynamics, dislocation theory, seismology and fibre wound composites. My interest in the subject of anisotropic wave motion had its origin in the study of small deformations superposed on large deformations of elastic solids. By varying the initial stretch in a homogeneously deformed solid, it is possible to synthesize aniso tropic materials whose elastic parameters vary continuously. The range of the parameter variation is limited by stability considerations in the case of small deformations super posed on large deformation problems and (what is essentially the same thing) by the of hyperbolicity (solids whose parameters allow wave motion) for anisotropic notion solids. The full implication of hyperbolicity for anisotropic elastic solids has never been previously examined, and even now the constraints which it imposes on the elasticity constants have only been examined for the class of transversely isotropic (hexagonal crystals) materials."

1. 1 Preface Many phenomena from physics, biology, chemistry and economics are modeled by di?erential equations with parameters. When a nonlinear equation is est- lished, its behavior/dynamics should be understood. In general, it is impossible to ?nd a complete dynamics of a nonlinear di?erential equation. Hence at least, either periodic or irregular/chaotic solutions are tried to be shown. So a pr- erty of a desired solution of a nonlinear equation is given as a parameterized boundary value problem. Consequently, the task is transformed to a solvability of an abstract nonlinear equation with parameters on a certain functional space. When a family of solutions of the abstract equation is known for some para- ters, the persistence or bifurcations of solutions from that family is studied as parameters are changing. There are several approaches to handle such nonl- ear bifurcation problems. One of them is a topological degree method, which is rather powerful in cases when nonlinearities are not enough smooth. The aim of this book is to present several original bifurcation results achieved by the author using the topological degree theory. The scope of the results is rather broad from showing periodic and chaotic behavior of non-smooth mechanical systems through the existence of traveling waves for ordinary di?erential eq- tions on in?nite lattices up to study periodic oscillations of undamped abstract waveequationsonHilbertspaceswithapplicationstononlinearbeamandstring partial di?erential equations. 1.

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.

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.

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.

The EUROMECH Colloquium "Dynamics of Vibro-Impact Systems" was held at th th Loughborough University on September 15 _18 , 1998. This was the flrst international meeting on this subject continuing the traditions of the series of Russian meetings held regularly since 1963. Mechanical systems with multiple impact interactions have wide applications in engineering as the most intensive sources of mechanical influence on materials, structures and processes. Vibro-impact systems are used widely in machine dynamics, vibration engineering, and structural mechanics. Analysis of vibro-impact systems involves the investigation of mathematical models with discontinuities and reveals their behaviour as strongly non-linear. Such systems exhibit complex resonances, synchronisation and pulling, bifurcations and chaos, exCitation of space coherent structures, shock waves, and solitons. The aim of the Colloquium was to facilitate the exchange of up-to-date information on the analysis and synthesis of vibro-impact systems as well as on the new developments in excitation, control and applications of vibro-impact processes.

The IUTAM Symposium on Advances in Nonlinear Stochastic Mechanics, held in Trondheim July 3-7, 1995, was the eighth of a series of IUTAM sponsored symposia which focus on the application of stochastic methods in mechanics. The previous meetings took place in Coventry, UK (1972), Sout'hampton, UK (1976), FrankfurtjOder, Germany (1982), Stockholm, Sweden (1984), Innsbruckjlgls, Austria (1987), Turin, Italy (1991) and San Antonio, Texas (1993). The symposium provided an extraordinary opportunity for scholars to meet and discuss recent advances in stochastic mechanics. The participants represented a wide range of expertise, from pure theoreticians to people primarily oriented toward applications. A significant achievement of the symposium was the very extensive discussions taking place over the whole range from highly theoretical questions to practical engineering applications. Several presentations also clearly demonstrated the substantial progress that has been achieved in recent years in terms of developing and implement ing stochastic analysis techniques for mechanical engineering systems. This aspect was further underpinned by specially invited extended lectures on computational stochastic mechanics, engineering applications of stochastic mechanics, and nonlinear active control. The symposium also reflected the very active and high-quality research taking place in the field of stochastic stability. Ten presentations were given on this topic ofa total of47 papers. A main conclusion that can be drawn from the proceedings of this symposium is that stochastic mechanics as a subject has reached great depth and width in both methodology and applicability.

This book concerns the numerical simulation of dynamical systems whose trajec- ries may not be differentiable everywhere. They are named nonsmooth dynamical systems. They make an important class of systems, rst because of the many app- cations in which nonsmooth models are useful, secondly because they give rise to new problems in various elds of science. Usually nonsmooth dynamical systems are represented as differential inclusions, complementarity systems, evolution va- ational inequalities, each of these classes itself being split into several subclasses. The book is divided into four parts, the rst three parts being sketched in Fig. 0. 1. The aim of the rst part is to present the main tools from mechanics and applied mathematics which are necessary to understand how nonsmooth dynamical systems may be numerically simulated in a reliable way. Many examples illustrate the th- retical results, and an emphasis is put on mechanical systems, as well as on electrical circuits (the so-called Filippov's systems are also examined in some detail, due to their importance in control applications). The second and third parts are dedicated to a detailed presentation of the numerical schemes. A fourth part is devoted to the presentation of the software platform Siconos. This book is not a textbook on - merical analysis of nonsmooth systems, in the sense that despite the main results of numerical analysis (convergence, order of consistency, etc. ) being presented, their proofs are not provided.

Cybernetical physics borrows methods from both theoretical physics and control engineering. It deals with the control of complex systems is one of the most important aspects in dealing with systems exhibiting nonlinear behavior or similar features that defy traditional control techniques. This book fully details this new discipline.

Following the recent developments in the field of absolute stability, Prof. Xiaoxin Liao, in conjunction with Prof. Pei Yu, has created a second edition of his seminal work on the subject. Liao begins with an introduction to the Lurie problem and Lurie control system, before moving on to the simple algebraic sufficient conditions for the absolute stability of autonomous and non-autonomous ODE systems, as well as several special classes of Lurie-type systems. The focus of the book then shifts toward the new results and research that have appeared in the decade since the first edition was published. This book is aimed to be used by undergraduates in the areas of applied mathematics, nonlinear control systems, and chaos control and synchronisation, but may also be useful as a reference for researchers and engineers. The book is self-contained, though a basic knowledge of calculus, linear system and matrix theory, and ordinary differential equations is a prerequisite.