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Author : Maurice Roseau
Publisher : Springer
ISBN 13 :
Total Pages : 276 pages
Book Rating : 4.3/5 (91 download)
Download or read book Vibrations non linéaires et théorie de la stabilité written by Maurice Roseau and published by Springer. This book was released on 1966 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Maurice Roseau
Publisher : Springer Science & Business Media
ISBN 13 : 3642615945
Total Pages : 530 pages
Book Rating : 4.6/5 (426 download)
Download or read book Vibrations in Mechanical Systems written by Maurice Roseau and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: The familiar concept described by the word "vibrations" suggests the rapid alternating motion of a system about and in the neighbourhood of its equilibrium position, under the action of random or deliberate disturbing forces. It falls within the province of mechanics, the science which deals with the laws of equilibrium, and of motion, and their applications to the theory of machines, to calculate these vibrations and predict their effects. While it is certainly true that the physical systems which can be the seat of vibrations are many and varied, it appears that they can be studied by methods which are largely indifferent to the nature of the underlying phenomena. It is to the development of such methods that we devote this book which deals with free or induced vibrations in discrete or continuous mechanical structures. The mathematical analysis of ordinary or partial differential equations describing the way in which the values of mechanical variables change over the course of time allows us to develop various theories, linearised or non-linearised, and very often of an asymptotic nature, which take account of conditions governing the stability of the motion, the effects of resonance, and the mechanism of wave interactions or vibratory modes in non-linear systems.
Author : D. D. Joseph
Publisher : Springer Science & Business Media
ISBN 13 : 3642809944
Total Pages : 290 pages
Book Rating : 4.6/5 (428 download)
Download or read book Stability of Fluid Motions II written by D. D. Joseph and published by Springer Science & Business Media. This book was released on 2013-03-07 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of stability aims at understanding the abrupt changes which are observed in fluid motions as the external parameters are varied. It is a demanding study, far from full grown, whose most interesting conclusions are recent. I have written a detailed account of those parts of the recent theory which I regard as established. Acknowledgements I started writing this book in 1967 at the invitation of Clifford Truesdell. It was to be a short work on the energy theory of stability and if I had stuck to that I would have finished the writing many years ago. The theory of stability has developed so rapidly since 1967 that the book I might then have written would now have a much too limited scope. I am grateful to Truesdell, not so much for the invitation to spend endless hours of writing and erasing, but for the generous way he has supported my efforts and encouraged me to higher standards of good work. I have tried to follow Truesdell's advice to write this work in a clear and uncomplicated style. This is not easy advice for a former sociologist to follow; if I have failed it is not due to a lack of urging by him or trying by me. My research during the years 1969-1970 was supported in part by a grant from the Guggenheim foundation to study in London.
Author : Wolfgang Hahn
Publisher : Springer Science & Business Media
ISBN 13 : 3642500854
Total Pages : 459 pages
Book Rating : 4.6/5 (425 download)
Download or read book Stability of Motion written by Wolfgang Hahn and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of the stability of motion has gained increasing signifi cance in the last decades as is apparent from the large number of publi cations on the subject. A considerable part of this work is concerned with practical problems, especially problems from the area of controls and servo-mechanisms, and concrete problems from engineering were the ones which first gave the decisin' impetus for the expansion and modern development of stability theory. In comparison with the many single publications, which are num bered in the thousands, the number of books on stability theory, and especially books not \\Titten in Russian, is extraordinarily small. Books which giw the student a complete introduction into the topic and which simultaneously familiarize him with the newer results of the theory and their applications to practical questions are completely lacking. I hope that the book which I hereby present will to some extent do justice to this double task. I haw endeavored to treat stability theory as a mathe matical discipline, to characterize its methods, and to prove its theorems rigorollsly and completely as mathematical theorems. Still I always strove to make reference to applications, to illustrate the arguments with examples, and to stress the interaction between theory and practice. The mathematical preparation of the reader should consist of about two to three years of university mathematics.
Author : Giancarlo Genta
Publisher : Springer Science & Business Media
ISBN 13 : 1468402366
Total Pages : 496 pages
Book Rating : 4.4/5 (684 download)
Download or read book Vibration of Structures and Machines written by Giancarlo Genta and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second edition follows the previous one after about two years. Apart from correcting a number of printing errors, few additions have been introduced. In the chapter on the finite element method, a short summary on finite elements in time (four-dimensional finite elements) has been introduced. In the chapter on rotordynamics, two new graphical representations are used; namely, the roots locus plot for free whirling and a tri-dimensional plot for the forced response for which the designation of "orbital tubes" has been proposed. The former has been borrowed from controlled systems dynamics, where it is widely used, while the latter is made practical by the availability of powerful graphical tools for postprocessing numerical or experimental results. As a last point, a more detailed description of the behaviour of magnetic bearings has been introduced in Chapter 6. Torino, September 1994 G. Genta Preface The present book originates from the need felt by the author to give a systematic form to the contents of the lectures he gives to mechanical and aeronautical engineering students of the Technical University (Politecnico) of Torino, within the frames of the courses of Principles and Methodologies of Mechanical Design and Construction of Aircraft Engines. Its main aim is that of summarizing the funda mentals of mechanics of vibrations to give the needed theoretical background to the engineer who has to deal with vibration analysis and to show a number of design applications of the theory.
Author : P Cvitanovic
Publisher : Routledge
ISBN 13 : 1351406035
Total Pages : 911 pages
Book Rating : 4.3/5 (514 download)
Download or read book Universality in Chaos, 2nd edition written by P Cvitanovic and published by Routledge. This book was released on 2017-07-12 with total page 911 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nature provides many examples of physical systems that are described by deterministic equations of motion, but that nevertheless exhibit nonpredictable behavior. The detailed description of turbulent motions remains perhaps the outstanding unsolved problem of classical physics. In recent years, however, a new theory has been formulated that succeeds in making quantitative predictions describing certain transitions to turbulence. Its significance lies in its possible application to large classes (often very dissimilar) of nonlinear systems. Since the publication of Universality in Chaos in 1984, progress has continued to be made in our understanding of nonlinear dynamical systems and chaos. This second edition extends the collection of articles to cover recent developments in the field, including the use of statistical mechanics techniques in the study of strange sets arising in dynamics. It concentrates on the universal aspects of chaotic motions, the qualitative and quantitative predictions that apply to large classes of physical systems. Much like the previous edition, this book will be an indispensable reference for researchers and graduate students interested in chaotic dynamics in the physical, biological, and mathematical sciences as well as engineering.
Author : George R. Gavalas
Publisher : Springer Science & Business Media
ISBN 13 : 3642876439
Total Pages : 116 pages
Book Rating : 4.6/5 (428 download)
Download or read book Nonlinear Differential Equations of Chemically Reacting Systems written by George R. Gavalas and published by Springer Science & Business Media. This book was released on 2013-03-13 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years considerable interest has developed in the mathe matical analysis of chemically reacting systems both in the absence and in the presence of diffusion. Earlier work has been limited to simple problems amenable to closed form solutions, but now the computer permits the numerical solution of complex systems of nonlinear differ ential equations. The numerical approach provides quantitative infor mation, but for practical reasons it must be limited to a rather narrow range of the parameters of the problem. Consequently, it is desirable to obtain broader qualitative information about the solutions by in vestigating from a more fundamental mathematical point of view the structure of the differential equations. This theoretical approach can actually complement and guide the computational approach by narrow ing down trial and error procedures, pinpointing singularities and suggesting methods for handling them. The study of the structure of the differential equations may also clarify some physical principles and suggest new experiments. A serious limitation ofthe theoretical approach is that many of the results obtained, such as the sufficient conditions for the stability of the steady state, turn out to be very conservative. Thus the theoretical and computational approaches are best used to gether for the purpose of understanding, designing, and controlling chemically reacting systems. The present monograph is intended as a contribution to the theory of the differential equations describing chemically reacting systems.
Author :
Publisher : Elsevier
ISBN 13 : 008087472X
Total Pages : 453 pages
Book Rating : 4.0/5 (88 download)
Download or read book Man under Vibration, Suffering and Protection written by and published by Elsevier. This book was released on 2009-06-01 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: Man under Vibration, Suffering and Protection
Author : C. Corduneanu
Publisher : American Mathematical Soc.
ISBN 13 : 0821846221
Total Pages : 205 pages
Book Rating : 4.8/5 (218 download)
Download or read book Principles of Differential and Integral Equations written by C. Corduneanu and published by American Mathematical Soc.. This book was released on 2008-05-09 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: In summary, the author has provided an elegant introduction to important topics in the theory of ordinary differential equations and integral equations. -- Mathematical Reviews This book is intended for a one-semester course in differential and integral equations for advanced undergraduates or beginning graduate students, with a view toward preparing the reader for graduate-level courses on more advanced topics. There is some emphasis on existence, uniqueness, and the qualitative behavior of solutions. Students from applied mathematics, physics, and engineering will find much of value in this book. The first five chapters cover ordinary differential equations. Chapter 5 contains a good treatment of the stability of ODEs. The next four chapters cover integral equations, including applications to second-order differential equations. Chapter 7 is a concise introduction to the important Fredholm theory of linear integral equations. The final chapter is a well-selected collection of fascinating miscellaneous facts about differential and integral equations. The prerequisites are a good course in advanced calculus, some preparation in linear algebra, and a reasonable acquaintance with elementary complex analysis. There are exercises throughout the text, with the more advanced of them providing good challenges to the student.
Author : David Yang Gao
Publisher : Springer Science & Business Media
ISBN 13 : 1461302757
Total Pages : 505 pages
Book Rating : 4.4/5 (613 download)
Download or read book Nonsmooth/Nonconvex Mechanics written by David Yang Gao and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonsmooth and nonconvex models arise in several important applications of mechanics and engineering. The interest in this field is growing from both mathematicians and engineers. The study of numerous industrial applications, including contact phenomena in statics and dynamics or delamination effects in composites, require the consideration of nonsmoothness and nonconvexity. The mathematical topics discussed in this book include variational and hemivariational inequalities, duality, complementarity, variational principles, sensitivity analysis, eigenvalue and resonance problems, and minimax problems. Applications are considered in the following areas among others: nonsmooth statics and dynamics, stability of quasi- static evolution processes, friction problems, adhesive contact and debonding, inverse problems, pseudoelastic modeling of phase transitions, chaotic behavior in nonlinear beams, and nonholonomic mechanical systems. This volume contains 22 chapters written by various leading researchers and presents a cohesive and authoritative overview of recent results and applications in the area of nonsmooth and nonconvex mechanics. Audience: Faculty, graduate students, and researchers in applied mathematics, optimization, control and engineering.
Author : Ingo Müller
Publisher : Springer Science & Business Media
ISBN 13 : 1468404474
Total Pages : 238 pages
Book Rating : 4.4/5 (684 download)
Download or read book Extended Thermodynamics written by Ingo Müller and published by Springer Science & Business Media. This book was released on 2013-03-08 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Physicists firmly believe that the differential equations of nature should be hyperbolic so as to exclude action at a distance; yet the equations of irreversible thermodynamics - those of Navier-Stokes and Fourier - are parabolic. This incompatibility between the expectation of physicists and the classical laws of thermodynamics has prompted the formulation of extended thermodynamics. After describing the motifs and early evolution of this new branch of irreversible thermodynamics, the authors apply the theory to mon-atomic gases, mixtures of gases, relativistic gases, and "gases" of phonons and photons. The discussion brings into perspective the various phenomena called second sound, such as heat propagation, propagation of shear stress and concentration, and the second sound in liquid helium. The formal mathematical structure of extended thermodynamics is exposed and the theory is shown to be fully compatible with the kinetic theory of gases. The study closes with the testing of extended thermodynamics through the exploitation of its predictions for measurements of light scattering and sound propagation.
Author : Harley Cohen
Publisher : Springer Science & Business Media
ISBN 13 : 1461395895
Total Pages : 194 pages
Book Rating : 4.4/5 (613 download)
Download or read book The Theory of Pseudo-rigid Bodies written by Harley Cohen and published by Springer Science & Business Media. This book was released on 2013-03-07 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph concerns the development, analysis, and application of the theory of pseudo-rigid bodies. It collects together our work on that subject over the last five years. While some results have appeared else where, much of the work is new. Our objective in writing this mono graph has been to present a new theory of the deformation of bodies, one that has not only a firm theoretical basis, but also the simplicity to serve as an effective tool in practical problems. Consequently, the main body of the treatise is a multifaceted development of the theory, from foundations to explicit solutions to linearizations to methods of approximation. The fact that this variety of aspects, each examined in considerable detail, can be collected together in a single, unified treat ment gives this theory an elegance that we feel sets it apart from many others. While our goal has always been to give a complete treatment of the theory as it now stands, the work here is not meant to be definitive. Theories are not entities that appear suddenly one day and thereafter stand as given. Rather, they must mature and grow with time and experience. Our development is more correctly a beginning, tempting others to explore, appraise, and modify its features so as to produce something better.
Author : G.P. Galdi
Publisher : Springer Science & Business Media
ISBN 13 : 0387941509
Total Pages : 362 pages
Book Rating : 4.3/5 (879 download)
Download or read book An Introduction to the Mathematical Theory of the Navier-Stokes Equations written by G.P. Galdi and published by Springer Science & Business Media. This book was released on 1994-04-28 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The volumes deal with the fundamental mathematical properties of the Navier-Stokes equations, such as existence, regularity and uniqueness of solutions, and, for unbounded domains, their asymptotic behavior. The work is an up-to-date and detailed investigation of these problems for motions in domains of different types: bounded, exterior and domain with noncompact boundaries. Throughout the work, main problems which, so far, remain open are pointed out and for some of these conjectures are offered. New results are presented throughout, while several classical subjects are treated in a completely original way."--Google Book Search.
Author : Giovanni Galdi
Publisher : Springer Science & Business Media
ISBN 13 : 1475738668
Total Pages : 476 pages
Book Rating : 4.4/5 (757 download)
Download or read book An Introduction to the Mathematical Theory of the Navier-Stokes Equations written by Giovanni Galdi and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: Undoubtedly, the Navier-Stokes equations are of basic importance within the context of modern theory of partial differential equations. Although the range of their applicability to concrete problems has now been clearly recognised to be limited, as my dear friend and bright colleague K.R. Ra jagopal has showed me by several examples during the past six years, the mathematical questions that remain open are of such a fascinating and challenging nature that analysts and applied mathematicians cannot help being attracted by them and trying to contribute to their resolution. Thus, it is not a coincidence that over the past ten years more than seventy sig nificant research papers have appeared concerning the well-posedness of boundary and initial-boundary value problems. In this monograph I shall perform a systematic and up-to-date investiga tion of the fundamental properties of the Navier-Stokes equations, including existence, uniqueness, and regularity of solutions and, whenever the region of flow is unbounded, of their spatial asymptotic behavior. I shall omit other relevant topics like boundary layer theory, stability, bifurcation, de tailed analysis of the behavior for large times, and free-boundary problems, which are to be considered "advanced" ones. In this sense the present work should be regarded as "introductory" to the matter.
Author : Vladimir Burd
Publisher : CRC Press
ISBN 13 : 158488875X
Total Pages : 357 pages
Book Rating : 4.5/5 (848 download)
Download or read book Method of Averaging for Differential Equations on an Infinite Interval written by Vladimir Burd and published by CRC Press. This book was released on 2007-03-19 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, mathematicians have detailed simpler proofs of known theorems, have identified new applications of the method of averaging, and have obtained many new results of these applications. Encompassing these novel aspects, Method of Averaging of the Infinite Interval: Theory and Applications rigorously explains the modern theory of the me
Author : Jorge Angeles
Publisher : Springer Science & Business Media
ISBN 13 : 1461239168
Total Pages : 149 pages
Book Rating : 4.4/5 (612 download)
Download or read book Rational Kinematics written by Jorge Angeles and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rational study of kinematics is a treatment of the subject based on invariants, i.e., quantities that remain essentially unchanged under a change of observer. An observer is understood to be a reference frame supplied with a clock (Truesdell 1966). This study will therefore include an introduction to invariants. The language of these is tensor analysis and multilinear algebra, both of which share many isomorphic relations, These subjects are treated in full detail in Ericksen (1960) and Bowen and Wang (1976), and hence will not be included here. Only a short account of notation and definitions will be presented. Moreover, definitions and basic concepts pertaining to the kinematics of rigid bodies will be also included. Although the kinematics of rigid bodies can be regarded as a particular case of the kinematics of continua, the former deserves attention on its own merits for several reasons. One of these is that it describes locally the motions undergone by continua. Another reason is that a whole area of mechanics, known as classical dynamics, is the study of the motions undergone by particles, rigid bodies, and systems thereof.
Author : William Strieder
Publisher : Springer Science & Business Media
ISBN 13 : 3642656242
Total Pages : 121 pages
Book Rating : 4.6/5 (426 download)
Download or read book Variational Methods Applied to Problems of Diffusion and Reaction written by William Strieder and published by Springer Science & Business Media. This book was released on 2013-03-07 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is an account of some problems involving diffusion or diffusion with simultaneous reaction that can be illuminated by the use of variational principles. It was written during a period that included sabbatical leaves of one of us (W. S. ) at the University of Minnesota and the other (R. A. ) at the University of Cambridge and we are grateful to the Petroleum Research Fund for helping to support the former and the Guggenheim Foundation for making possible the latter. We would also like to thank Stephen Prager for getting us together in the first place and for showing how interesting and useful these methods can be. We have also benefitted from correspondence with Dr. A. M. Arthurs of the University of York and from the counsel of Dr. B. D. Coleman the general editor of this series. Table of Contents Chapter 1. Introduction and Preliminaries . 1. 1. General Survey 1 1. 2. Phenomenological Descriptions of Diffusion and Reaction 2 1. 3. Correlation Functions for Random Suspensions 4 1. 4. Mean Free Path Statistics . 8 1. 5. Void Point-Surface Statistics . 11 1. 6. Variational Principles Applied to the Diffusion Equation. 12 1. 7. Notation. 16 Chapter 2. Diffusion Through a Porous Medium . 18 2. 1. Introduction 18 2. 2. Diffusion Through an Isotropic Porous Medium 18 2. 3. Variational Formulation for De . 20 2. 4. Bounds on De for an Isotropic Suspension 22 2. 5.
