This 2006 book presents a systematic introduction to the theory of parametric stability of structures under both deterministic and stochastic loadings. A comprehensive range of theories are presented and various application problems are formulated and solved, often using more than one approach. Investigation of an elastic system's dynamic stability frequently leads to the study of dynamic behaviour of the solutions of parametrically excited systems. Parametric instability or resonance is more dangerous than ordinary resonance as it is characterised by exponential growth of the response amplitudes even in the presence of damping. The emphasis in this book is on the applications and various analytical and numerical methods for solving engineering problems. The materials presented are as self-contained as possible, with all of the important steps of analysis provided in order to make the book suitable as a graduate-level textbook and especially for self-study.

The need for a general collection of electroacoustical reference and design data in graphical form has been felt by acousticians and engineers for some time. This type of data can otherwise only be found in a collection of handbooks. Therefore, it is the author's intention that this book serve as a single source for many electroacoustical reference and system design requirements. In form, the volume closely resembles Frank Massa's Acoustic Design Charts, a handy book dating from 1942 that has long been out of print. The basic format of Massa's book has been followed here: For each entry, graphical data are presented on the right page, while text, examples, and refer ences appear on the left page. In this manner, the user can solve a given problem without thumbing from one page to the next. All graphs and charts have been scaled for ease in data entry and reading. The book is divided into the following sections: A. General Acoustical Relationships. This section covers the behavior of sound transmis sion in reverberant and free fields, sound absorption and diffraction, and directional characteris tics of basic sound radiators. B. Loudspeakers. Loudspeakers are discussed in terms of basic relationships regarding cone excursion, sensitivity, efficiency, and directivity index, power ratings, and architectural layout. c. Microphones. The topics in this section include microphone sensitivity and noise rating, analysis of directional properties, stereo microphone array characteristics, proximity effects, and boundary conditions. D. Signal Transmission."

This is a textbook for a first course in mechanical vibrations. There are many books in this area that try to include everything, thus they have become exhaustive compendiums, overwhelming for the undergraduate. In this book, all the basic concepts in mechanical vibrations are clearly identified and presented in a concise and simple manner with illustrative and practical examples. Vibration concepts include a review of selected topics in mechanics; a description of single-degree-of-freedom (SDOF) systems in terms of equivalent mass, equivalent stiffness, and equivalent damping; a unified treatment of various forced response problems (base excitation and rotating balance); an introduction to systems thinking, highlighting the fact that SDOF analysis is a building block for multi-degree-of-freedom (MDOF) and continuous system analyses via modal analysis; and a simple introduction to finite element analysis to connect continuous system and MDOF analyses. There are more than sixty exercise problems, and a complete solutions manual. The use of MATLAB (R) software is emphasized.

Interest in acoustics continues to increase. Although this branch of science was concerned primarily with the promotion of qualitative and quantitative sound transmission until a few decades ago, emphasis is currently placed also on the limitation of sound nuisance and, by extension, the setting of boundaries for permissible sound levels in places \vhere people are found. This last aspect in particular is exercising more and more influence on the design of buildings and machines, and in town and country planning. In addition, sound vibrations, because of their physical characteristics, are being used increasingly in disparate disciplines such as navigation, medical investigation and non destructive materials research. The flood of publications resulting from this increased interest in acoustics has led to a growing number of people being confronted with terminology which had until quite re cently only been used by a relatively small group of specialists and had remained largely unknown as a result. This four language dictionary, based on 'W. Reichardt, Technische Akustik; Berlin 1979', has been compiled to make not only this literature but also the nomenclature of equipment and instructions for their use accessible to the specialist and the interested layman."

Shear waves and closely related interface waves (Rayleigh, Stoneley and Scholte) play an important role in many areas of engineering, geophysics and underwater acoustics. In some cases interest is focused on large-amplitude waves of low frequency such as those associ ated with earthquakes and nuclear explosions; in other cases low amplitude waves, which have often travelled great distances through the sediment, are of interest. Both low and high frequency shear and interface waves are often used for seafloor probing and sediment characterization. As a result of the wide spectrum of different interests, different disciplines have developed lines of research and a literature particularly suited to their own problems. For example water-column acousticians view the seafloor sediment as the lower boundary of their domain and are interested in shear and interface waves in the near bottom sediments mainly from the standpoint of how they influence absorption and reflection at this boundary. On the other hand, geophysicists seeking deep oil deposits are interested in the maximum penetration into the sediments and the tell-tale characteristics of the seismic waves that have encountered potential oil or gas bearing strata. In another area, geotechnical engineers use shear and interface waves to study soil properties necessary for the design and the siting of seafloor structures.

A systematic treatment of current crashworthiness practice in the automotive, railroad and aircraft industries. Structural, exterior and interior design, occupant biomechanics, seat and restraint systems are dealt with, taking account of statistical data, current regulations and state-of-the-art design tool capabilities. Occupant kinematics and biomechanics are reviewed, leading to a basic understanding of human tolerance to impact and of the use of anthropometric test dummies and mathematical modelling techniques. Different types of restraining systems are described in terms of impact biomechanics. The material and structural behaviour of vehicle components is discussed in relation to crash testing. A variety of commonly used techniques for simulating occupants and structures are presented, in particular the use of multibody dynamics, finite element methods and simplified macro-elements, in the context of design tools of increasing complexity, which can be used to model both vehicles and occupants. Audience: An excellent reference for researchers, engineers, students and all other professionals involved in crashworthiness work.

Thisvolumecontainsacollectionofpapersbyinternationalexpertsingeoph- ical ?uid dynamics, based upon presentations at a colloquium held in memory of Pedro Ripa on the ?rst anniversary of his untimely death. They review or present recent developments in hydrodynamic stability theory, Hamiltonian ?uid mechanics, balanceddynamics, waves, vortices, generaloceanographyand the physical oceanography of the Gulf ofCalifornia; all of them subjects in which Professor Ripamadeimportant contributions. His work, but also his friendly spiritandkindnesswerehighly regardedandappreciatedby colleagues and students alike around the world. This book is a tribute to his scienti?c legacy and constitutes a valuable reference for researchers and graduate s- dents interested in geophysical and general ?uid mechanics. Earlyin his career asa physicaloceanographer, Pedro Ripa made two la- mark contributions to geophysical ?uid dynamics. In 1981, he showed that the conservation of the potential vorticity is related to the invariance of the eq- tions of motion under the symmetry transformationsof the labels that identify the ?uid particles. That is, potential vorticity conservation is a consequence, via Noether's theorem, of the particle re-labelling symmetry. Two years later he published a paper entitled "General stability conditions for zonal ?ows in a one-layer model on the beta-plane or the sphere," where he established nec- sary conditions for stability in the shallow water equations, nowadays known as "Ripa's Theorem. " This is one of the very few Arnol'd-like stability con- tions that goes beyond two-dimensional or quasi-geostrophic ?ow, and stands alongside other famous stability criteria in making the foundations of the ?eld.

This book is primarily a research monograph that presents in a unified man ner some recent research on a class of hybrid dynamical systems (HDS). The book is intended both for researchers and advanced postgraduate stu dents working in the areas of control engineering, theoretical computer science, or applied mathematics and with an interest in the emerging field of hybrid dynamical systems. The book assumes competence in the basic mathematical techniques of modern control theory. The material presented in this book derives from a period of fruitful research collaboration between the authors that began in 1994 and is still ongoing. Some of the material contained herein has appeared as isolated results in journal papers and conference proceedings. This work presents this material in an integrated and coherent manner and also presents many new results. Much of the material arose from joint work with students and colleagues, and the authors wish to acknowledge the major contributions made by Ian Petersen, Efstratios Skafidas, Valery Ugrinovskii, David Cook, Iven Mareels, and Bill Moran. There is currently no precise definition of a hybrid dynamical system; however, in broad terms it is a dynamical system that involves a mixture of discrete-valued and continuous-valued variables. Since the early 1990s, a bewildering array of results have appeared under the umbrella of HDS, ranging from the analysis of elementary on-off control systems to sophis ticated mathematical logic-based descriptions of large real-time software systems.

"Energy Methods in Dynamics "is a textbook based on the lectures given by the first author at Ruhr University Bochum, Germany. Its aim is to help students acquire both a good grasp of the first principles from which the governing equations can be derived, and the adequate mathematical methods for their solving. Its distinctive features, as seen from the title, lie in the systematic and intensive use of Hamilton's variational principle and its generalizations for deriving the governing equations of conservative and dissipative mechanical systems, and also in providing the direct variational-asymptotic analysis, whenever available, of the energy and dissipation for the solution of these equations. It demonstrates that many well-known methods in dynamics like those of Lindstedt-Poincare, Bogoliubov-Mitropolsky, Kolmogorov-Arnold-Moser (KAM), Wentzel Kramers Brillouin (WKB), and Whitham are derivable from this variational-asymptotic analysis.

This second edition includes the solutions to all exercises as well as some new materials concerning amplitude and slope modulations of nonlinear dispersive waves."

This text is an introduction to the feedback control of lightly damped flexible structures; the emphasis is placed on basic issues such as actuator and sensor selection, placement and dynamics, and actual implementation for solving practical problems. The book consists of 11 chapters; in chapters 2 to 5, the open-loop transfer functions of various active structures are derived from their constitutive equations; the discussion includes a truss and sandwich beams and plates with embedded piezoelectric actuators and sensors. The virtues of collocated actuator-sensor configurations are pointed out and used to develop active damping with guaranteed stability. Chapters 6 to 8 are devoted to the model-based control of SISO systems; optimal control is developed graphically using the symmetric root locus; the gain-phase relationship is discussed and the design tradeoffs are explained in the frequency domain. The issues of robustness with respect to the parametric uncertainty and the spillover instability are examined. After two short chapters on controllability (ch. 9) and stability (ch. 10), the book concludes with a set of applications to active damping and precision positioning of a set of aerospace, mechanical and civil engineering structures. The book is intended for structural engineers who want to acquire some background in vibration control; it can be used as a textbook for a graduate course on vibration control or active structures. The text is supplemented with 98 problems.

In this book several connections between probability theory and wave propagation are explored. The connection comes via the probabilistic (or path integral) representation of both the (fixed frequency) Green functions and of the propagators -operators mapping initial into present time data. The formalism includes both waves in continuous space and in discrete structures.
One of the main applications of the formalism developed is to inverse problems in wave propagation. Using the probabilistic formalism, the parameters of the medium and the surfaces determining the region of propagation appear explicitly in the path integral representation of the Green functions and propagators. This fact is what provides a useful starting point for inverse problem formulation.

Audience: The book is suitable for advanced graduate students in the mathematical, physical or in the engineering sciences. The presentation is quite self-contained, and not extremely rigorous.

Multibody dynamics started with the ideas of Jacob and Daniel Bernoul li and later on with d'Alembert's principle. In establishing a solution for the problem of the center of oscillation for a two-mass-pendulum Jacob Ber noulli spoke about balancing the profit-and-Ioss account with respect to the motion of the two masses. Daniel Bernoulli extended these ideas to a chain pendulum and called forces not contributing to the motion "lost forces," thus being already very close to d'Alembert's principle. D'Alembert considered a "system of bodies, which are interconnected in some arbitrary way. " He suggested separating the motion into two parts, one moving, the other being at rest. In modern terms, or at least in terms being applied in engineering mechanics, this means that the forces acting on a system of bodies are split into active and passive forces. Active forces generate motion, passive forces do not; they are a result of constraints. This interpretation of d'Alembert's principle is due to Lagrange and up to now has been the basis of multi body dynamics (D' Alembert, Traite de Dynamique, 1743; Lagrange, Mecanique Analytique, 1811). Thus, multibody dynamics started in France. During the nineteenth century there were few activities in the multi body field even though industry offered plenty of possible applications and famous re presentatives of mechanics were aware of the problems related to multibody dynamics. Poisson in his "Traite de Mecanique" (Paris 1833) gave an im pressive description of these problems, including impacts and friction."

Advances in computational mechanics can only be achieved on the basis of fruitful discussion between researchers and practising engineers. This has been achieved in the present publication, which contains all the papers presented at the first International DIANA Conference on Computational Mechanics. Nearly all papers show the results of calculations achieved with the DIANATM Finite Element System. Broadly, the book follows the line of research from the material level, via the element level, to the structural level. But it should be emphasised that much current research passes from one level to the other, and such an interaction is also reflected here. The following domains are treated: (hyper)elasticity, (visco)plasticity and cracking; (enriched) damaging continua models; material experiments vs. computational models; stochastic approaches; fluid--structure interactions; element technology; geometrical nonlinearity and structural instability; nonlinear dynamics; solution procedures.

In this book, regular structures are de ned as periodic structures consisting of repeated elements (translational symmetry) as well as structures with a geom- ric symmetry. Regular structures have for a long time been attracting the attention of scientists by the extraordinary beauty of their forms. They have been studied in many areas of science: chemistry, physics, biology, etc. Systems with geometric symmetry are used widely in many areas of engineering. The various kinds of bases under machines, cyclically repeated forms of stators, reduction gears, rotors with blades mounted on them, etc. represent regular structures. The study of real-life engineering structures faces considerable dif culties because they comprise a great number of working mechanisms that, in turn, consist of many different elastic subsystems and elements. The computational models of such systems represent a hierarchical structure and contain hundreds and thousands of parameters. The main problems in the analysis of such systems are the dim- sion reduction of model and revealing the dominant parameters that determine its dynamics and form its energy nucleus. The two most widely used approaches to the simulation of such systems are as follows: 1. Methods using lumped parameters models, i.e., a discretization of the original system and its representation as a system with lumped parameters [including nite-element method (FEM)]. 2. The use of idealized elements with distributed parameters and known analytical solutions for both the local elements and the subsystems.

During the last decades, applications of dynamical analysis in advanced, often nonlinear, engineering systems have been evolved in a revolutionary way. In this context one can think of applications in aerospace engineering like satellites, in naval engineering like ship motion, in mechanical engineering like rotating machinery, vehicle systems, robots and biomechanics, and in civil engineering like earthquake dynamics and offshore technology. One could continue with this list for a long time. The application of advanced dynamics in the above fields has been possible due to the use of sophisticated computational techniques employing powerful concepts of nonlinear dynamics. These concepts have been and are being developed in mathematics, mechanics and physics. It should be remarked that careful experimental studies are vitally needed to establish the real existence and observability of the predicted dynamical phenomena. The interaction between nonlinear dynamics and nonlinear control in advanced engineering systems is becoming of increasing importance because of several reasons. Firstly, control strategies in nonlinear systems are used to obtain desired dynamic behaviour and improved reliability during operation, Applications include power plant rotating machinery, vehicle systems, robotics, etc. Terms like motion control, optimal control and adaptive control are used in this field of interest. Since mechanical and electronic components are often necessary to realize the desired action in practice, the engineers use the term mechatronics to indicate this field. If the desired dynamic behaviour is achieved by changing design variables (mostly called system parameters), one can think of fields like control of chaos.

"Symposium Transsonicum" was founded by Klaus Oswatitsch four decades ago when there was clearly a need for a systematic treatment of flow problems in the higher speed regime in aeronautics. The first conference in 1962 brought together scientists concerned with fundamental problems involving the sonic flow speed regime. Results of the conference provided an understanding of some basic tran sonic phenomena by proposing mathematical methods that allowed for the de velopment of practical calculations. The "Transonic Controversy" (about shock free flows) was still an open issue after this meeting. In 1975 the second symposium was held, by then there was much understanding in how to avoid shocks in a steady plane flow to be designed, but still very little was known in unsteady phenomena due to a lack of elucidating experiments. A third meeting in 1988 reflected the availability oflarger computers which allowed the numerical analysis of flows with shocks to a reasonable accuracy. Because we are trying to keep Oswatitsch's heritage in science alive especially in Gottingen, we were asked by the aerospace research community to organize another symposium. Much had been achieved already in the knowledge, techno logy and applications in transonics, so IUT AM had to be convinced that a fourth meeting would not just be a reunion of old friends reminiscing some scientific past. The scientific committee greatly supported my efforts to invite scientists ac tively working in transonic problems which still pose substantial difficulties to ae rospace and turbomachinery industry."

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.

... a wise man knows all things in a manner in which this is possible, not, however, knowing them individually. Aristotle. Metaphysics * The problem of consideration of vortex fields' influence on solid body dynamics has a long history. One constantly comes upon it in flight dynamics of airplanes, helicopters, and other flying vehicles (FV) moving in the atmosphere, in dynamics of ships with hydrofoils, and in dynamics of rocket carriers (RC) and spacecrafts (SC) with liquid-propellant rocket engines (LPRE), that are equipped with special damping devices and other structural elements inside fluid tanks. Similar problems occur when solving problems related to attitude control and stabilization of artificial Earth satellites (AES) and spacecrafts with magnetic (electro magnetic) systems, in conducting elements of which eddy currents are induced while control of those vehicles' angular position. It is also true with special test facilities for dynamic testing of space vehicles and their systems, with modern high-speed magnetic suspension transport systems (those based on the phenomenon of 'magnetic levitation'), with generators having rotors carried in 'magnetic bearings', and so on."

This is the second and final issue of the collection of papers that were contributed by friends and colleagues of (Late) Professor P. R. "Pat" Sethna of the University of Minnesota to commemorate his 70th birthday on May 26, 1993. The first set of contributions was published in Nonlinear Dynamics as the last issue (no. 6) of Vol. 4 in 1993. As circumstances would have it, Professor Sethna was diagnosed with cancer in the fall of 1992 and, after an extended battle with the disease, he passed away on November 4, 1993, just a few days before the first set of contributed papers appeared in print. It is gratifying to report that the organizers of these vi Foreword commemorative issues in Nonlinear Dynamics were able to present to Professor Sethna, on the occasion of his 70th birthday, complete details of the planned commemorative issues. This second set of contributions is dedicated, in memoriam, to Professor P. R. Sethna. As many of you are well aware, Professor Sethna was an active researcher in the field of nonlinear vibrations and dynamics for nearly forty years, making many fundamental and significant contributions to both the theoretical and applied aspects of this field. He was also recognized for his outstanding leadership and administrative abilities, amply demonstrated through his position as the Head of the Department of Aerospace Engineering and Mechanics at the University of Minnesota for twenty-six years (1966-1992).

Ad ap tive Contro l provid es tec hniques for aut omatic adjustment in real t ime of cont roller parameter s in order to achieve or to maintain a desired level for the performance of cont rol systems when the dyn amic param et ers of t he process are unknown and/or var y in time. These techniques have as a main feature t he abilit y to ext ract significant information from real dat a in ord er to tune the cont roller and they feature a me chanism for adjust ing parameter s (of a plant model or of a cont roller). While the history of Adaptive Control is lon g, significant progr ess in under - standing and applying Adaptive Con trol began in the early sevent ies. The growing availability of digital com puters have also contributed to the devel- opment of the field . The earlier applicat ions in the sevent ies and beginning of the eight ies, provided important feedback for the development of the field . Theoretical developments allowed a number of basic problems to be solved . The aim of this book is to provide a coherent and comprehensive treatment of the field . The presentation takes the read er from the basic problem formu- lation to the analytical solutions who se prac tical significance is illustrated by applications.

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.

Linear acoustics was thought to be fully encapsulated in physics texts of the 1950s, but this view has been changed by developments in physics during the last four decades. There is a significant new amount of theory that can be used to address problems in linear acoustics and vibration, but only a small amount of reported work does so. This book is an attempt to bridge the gap between theoreticians and practitioners, as well as the gap between quantum and acoustic. Tutorial chapters provide introductions to each of the major aspects of the physical theory and are written using the appropriate terminology of the acoustical community. The book will act as a quick-start guide to the new methods while providing a wide-ranging introduction to the physical concepts.

The increased level of activity on structural health monitoring (SHM) in various universities and research labs has resulted in the development of new methodologies for both identifying the existing damage in structures and predicting the onset of damage that may occur during service. Designers often have to consult a variety of textbooks, journal papers and reports, because many of these methodologies require advanced knowledge of mechanics, dynamics, wave propagation, and material science. Computational Techniques for Structural Health Monitoring gives a one-volume, in-depth introduction to the different computational methodologies available for rapid detection of flaws in structures. Techniques, algorithms and results are presented in a way that allows their direct application. A number of case studies are included to highlight further the practical aspects of the selected topics. Computational Techniques for Structural Health Monitoring also provides the reader with numerical simulation tools that are essential to the development of novel algorithms for the interpretation of experimental measurements, and for the identification of damage and its characterization. Upon reading Computational Techniques for Structural Health Monitoring, graduate students will be able to begin research-level work in the area of structural health monitoring. The level of detail in the description of formulation and implementation also allows engineers to apply the concepts directly in their research.

By providing all the basic knowledge needed to assess how useful active noise control will be for a given problem, this book assists in the designing, setting up, and tuning of an active noise-control system. Written for students who have no prior knowledge of acoustics, signal processing, or noise control but who do have a reasonable grasp of basic physics and mathematics, the text is short and descriptive, leaving all mathematical details and proofs concerning vibrations, signal processing and the like to more advanced texts or research monographs. The book can thus be used in independent study, in a classroom with laboratories, or in conjunction with a kit for experiment or demonstration. Topics covered include basic acoustics, human perception and sound, sound intensity and related concepts, fundamentals of passive noise- control strategies, basics of digital systems and adaptive controllers, and active noise control systems.

The main objective of the First International Symposium on Lubricated Transport of Viscous Materials was to bring together scientists and engineers from academia and industryto discuss current research work and exchange ideas in this newly emerging field. It is an area offluid dynamics devoted to laying bare the principlesofthe lubricated transport of viscous materials such as crude oil, concentrated oil/water emulsion, slurries and capsules. It encompasses several types of problem. Studies of migration of particulates away from walls, Segre-Silverberg effects, lubrication versus lift and shear-induced migration belong to one category. Some of the technological problems are the fluid dynamics ofcore flows emphasizing studies ofstability, problems of start-up, lift-off and eccentric flow where gravity causes the core flow to stratify. Another category of problems deals with the fouling of pipe walls with oil, with undesirable increases in pressure gradients and even blocking. This study involves subjects like adhesion and dynamic contact angles. The topics ofshear-induced diffusion ofsmall particles and wall slip in slow flow are other appropriate subjects. Computer intensive studiesofflow-induced microstructures and moving interface problems are yet additional research directions. The general consensus was that the Symposium was a tremendous success, although the number of presentations fell below expectations. Scientists from the petroleum industry, and this includes INTEVEP (Venezuela), Schlumberger and Syncrude Canada Ltd., and consultants to oil companies actively participated in the Symposium. The meeting produced new insights which should lead to further interesting research work and established contacts for possiblejoint investigations."