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.

While the stability theory for systems with bilateral constraints is a well-established field, this monograph represents a systematic study of mechanical systems with unilateral constraints, such as unilateral contact, impact and friction. Such unilateral constraints give rise to non-smooth dynamical models for which stability theory is developed in this work. The book will be of interest to those working in the field of non-smooth mechanics and dynamics.

This book deals with the class of singular systems with random abrupt changes also known as singular Markovian jump systems. Various problems and their robustness are tackled. The book examines both the theoretical and practical aspects of the control problems from the angle of the structural properties of linear systems. It can be used as a textbook as well as a reference for researchers in control or mathematics with interest in control theory.

1. Background This textbook is an introduction to and exploration of a number of core topics in the ?eld of applied mechanics. Mechanics, in both its theoretical and applied contexts, is, like all scienti?c endeavors, a human construct. It re?ects the personalities, thoughts, errors, and successes of its creators. We therefore provide some personal information about each of these individuals when their names arise for the ?rst time in this book. This should enable the reader to piece together a cultural-historical picture of the ?eld s origins and development. This does not mean that we are writing history. Nevertheless, some remarks putting individuals and ideas in context are necessary in order to make clear what we are speaking about - and what we are not speaking about. At the end of the 19th century, technical universities were established eve- where in Europe in an almost euphoric manner. But the practice of technical mechanics itself, as one of the basics of technical development, was in a desolate state, due largely to the refusal of its practitioners to recognize the in?uence of kinetics on motion. They were correct to the extend that then current mechanical systems moved with small velocities where kinetics does not play a signi?cant role. But they had failed to keep up with developments in the science underlying their craft and were unable to keep pace with the speeds of such systems as the steam engine.

Unlike the conventional research for the general theory of stability, this mono graph deals with problems on stability and stabilization of dynamic systems with respect not to all but just to a given part of the variables characterizing these systems. Such problems are often referred to as the problems of partial stability (stabilization). They naturally arise in applications either from the requirement of proper performance of a system or in assessing system capa bility. In addition, a lot of actual (or desired) phenomena can be formulated in terms of these problems and be analyzed with these problems taken as the basis. The following multiaspect phenomena and problems can be indicated: * "Lotka-Volterra ecological principle of extinction;" * focusing and acceleration of particles in electromagnetic fields; * "drift" of the gyroscope axis; * stabilization of a spacecraft by specially arranged relative motion of rotors connected to it. Also very effective is the approach to the problem of stability (stabilization) with respect to all the variables based on preliminary analysis of partial sta bility (stabilization). A. M. Lyapunov, the founder of the modern theory of stability, was the first to formulate the problem of partial stability. Later, works by V. V. Rumyan tsev drew the attention of many mathematicians and mechanicians around the world to this problem, which resulted in its being intensively worked out. The method of Lyapunov functions became the key investigative method which turned out to be very effective in analyzing both theoretic and applied problems.

Micromechanics provides a link between the structure and the properties at different scales of observation. This book deals with micromechanical analysis of interfaces and interface layers and presents several modelling tools. These range from the rigorous method of asymptotic expansions to practical finite element simulations, suitable for this class of problems. The corresponding two parts of the book are self-contained, so they can be read separately.