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Nonlinear Vibrations And The Wave Equation
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Book Synopsis Nonlinear Vibrations and the Wave Equation by : Alain Haraux
Download or read book Nonlinear Vibrations and the Wave Equation written by Alain Haraux and published by Springer. This book was released on 2018-05-02 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers the revised lecture notes from a seminar course offered at the Federal University of Rio de Janeiro in 1986, then in Tokyo in 1987. An additional chapter has been added to reflect more recent advances in the field.
Book Synopsis Nonlinear Oscillations of Hamiltonian PDEs by : Massimiliano Berti
Download or read book Nonlinear Oscillations of Hamiltonian PDEs written by Massimiliano Berti and published by Springer Science & Business Media. This book was released on 2007-10-01 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many partial differential equations (PDEs) that arise in physics can be viewed as infinite-dimensional Hamiltonian systems. This monograph presents recent existence results of nonlinear oscillations of Hamiltonian PDEs, particularly of periodic solutions for completely resonant nonlinear wave equations. The text serves as an introduction to research in this fascinating and rapidly growing field. Graduate students and researchers interested in variational techniques and nonlinear analysis applied to Hamiltonian PDEs will find inspiration in the book.
Book Synopsis Understanding Acoustics by : Steven L. Garrett
Download or read book Understanding Acoustics written by Steven L. Garrett and published by Springer. This book was released on 2017-02-24 with total page 913 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a unified approach to acoustics and vibration suitable for use in advanced undergraduate and first-year graduate courses on vibration and fluids. The book includes thorough treatment of vibration of harmonic oscillators, coupled oscillators, isotropic elasticity, and waves in solids including the use of resonance techniques for determination of elastic moduli. Drawing on 35 years of experience teaching introductory graduate acoustics at the Naval Postgraduate School and Penn State, the author presents a hydrodynamic approach to the acoustics of sound in fluids that provides a uniform methodology for analysis of lumped-element systems and wave propagation that can incorporate attenuation mechanisms and complex media. This view provides a consistent and reliable approach that can be extended with confidence to more complex fluids and future applications. Understanding Acoustics opens with a mathematical introduction that includes graphing and statistical uncertainty, followed by five chapters on vibration and elastic waves that provide important results and highlight modern applications while introducing analytical techniques that are revisited in the study of waves in fluids covered in Part II. A unified approach to waves in fluids (i.e., liquids and gases) is based on a mastery of the hydrodynamic equations. Part III demonstrates extensions of this view to nonlinear acoustics. Engaging and practical, this book is a must-read for graduate students in acoustics and vibration as well as active researchers interested in a novel approach to the material.
Book Synopsis Nonlinear Diffusion Equations and Their Equilibrium States II by : W.-M. Ni
Download or read book Nonlinear Diffusion Equations and Their Equilibrium States II written by W.-M. Ni and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years considerable interest has been focused on nonlinear diffu sion problems, the archetypical equation for these being Ut = ~U + f(u). Here ~ denotes the n-dimensional Laplacian, the solution u = u(x, t) is defined over some space-time domain of the form n x [O,T], and f(u) is a given real function whose form is determined by various physical and mathematical applications. These applications have become more varied and widespread as problem after problem has been shown to lead to an equation of this type or to its time-independent counterpart, the elliptic equation of equilibrium ~u+f(u)=O. Particular cases arise, for example, in population genetics, the physics of nu clear stability, phase transitions between liquids and gases, flows in porous media, the Lend-Emden equation of astrophysics, various simplified com bustion models, and in determining metrics which realize given scalar or Gaussian curvatures. In the latter direction, for example, the problem of finding conformal metrics with prescribed curvature leads to a ground state problem involving critical exponents. Thus not only analysts, but geome ters as well, can find common ground in the present work. The corresponding mathematical problem is to determine how the struc ture of the nonlinear function f(u) influences the behavior of the solution.
Book Synopsis Harmonic Balance for Nonlinear Vibration Problems by : Malte Krack
Download or read book Harmonic Balance for Nonlinear Vibration Problems written by Malte Krack and published by Springer. This book was released on 2019-03-23 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents an introduction to Harmonic Balance for nonlinear vibration problems, covering the theoretical basis, its application to mechanical systems, and its computational implementation. Harmonic Balance is an approximation method for the computation of periodic solutions of nonlinear ordinary and differential-algebraic equations. It outperforms numerical forward integration in terms of computational efficiency often by several orders of magnitude. The method is widely used in the analysis of nonlinear systems, including structures, fluids and electric circuits. The book includes solved exercises which illustrate the advantages of Harmonic Balance over alternative methods as well as its limitations. The target audience primarily comprises graduate and post-graduate students, but the book may also be beneficial for research experts and practitioners in industry.
Book Synopsis Linear and Nonlinear Waves by : G. B. Whitham
Download or read book Linear and Nonlinear Waves written by G. B. Whitham and published by John Wiley & Sons. This book was released on 2011-10-18 with total page 660 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now in an accessible paperback edition, this classic work is just as relevant as when it first appeared in 1974, due to the increased use of nonlinear waves. It covers the behavior of waves in two parts, with the first part addressing hyperbolic waves and the second addressing dispersive waves. The mathematical principles are presented along with examples of specific cases in communications and specific physical fields, including flood waves in rivers, waves in glaciers, traffic flow, sonic booms, blast waves, and ocean waves from storms.
Book Synopsis Vibrations and Waves in Continuous Mechanical Systems by : Peter Hagedorn
Download or read book Vibrations and Waves in Continuous Mechanical Systems written by Peter Hagedorn and published by John Wiley & Sons. This book was released on 2007-10-22 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of vibrations is of fundamental importance in engineering and technology. Discrete modelling is sufficient to understand the dynamics of many vibrating systems; however a large number of vibration phenomena are far more easily understood when modelled as continuous systems. The theory of vibrations in continuous systems is crucial to the understanding of engineering problems in areas as diverse as automotive brakes, overhead transmission lines, liquid filled tanks, ultrasonic testing or room acoustics. Starting from an elementary level, Vibrations and Waves in Continuous Mechanical Systems helps develop a comprehensive understanding of the theory of these systems and the tools with which to analyse them, before progressing to more advanced topics. Presents dynamics and analysis techniques for a wide range of continuous systems including strings, bars, beams, membranes, plates, fluids and elastic bodies in one, two and three dimensions. Covers special topics such as the interaction of discrete and continuous systems, vibrations in translating media, and sound emission from vibrating surfaces, among others. Develops the reader’s understanding by progressing from very simple results to more complex analysis without skipping the key steps in the derivations. Offers a number of new topics and exercises that form essential steppingstones to the present level of research in the field. Includes exercises at the end of the chapters based on both the academic and practical experience of the authors. Vibrations and Waves in Continuous Mechanical Systems provides a first course on the vibrations of continuous systems that will be suitable for students of continuous system dynamics, at senior undergraduate and graduate levels, in mechanical, civil and aerospace engineering. It will also appeal to researchers developing theory and analysis within the field.
Book Synopsis Nonlinear Oscillations and Waves in Dynamical Systems by : P.S Landa
Download or read book Nonlinear Oscillations and Waves in Dynamical Systems written by P.S Landa and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rich variety of books devoted to dynamical chaos, solitons, self-organization has appeared in recent years. These problems were all considered independently of one another. Therefore many of readers of these books do not suspect that the problems discussed are divisions of a great generalizing science - the theory of oscillations and waves. This science is not some branch of physics or mechanics, it is a science in its own right. It is in some sense a meta-science. In this respect the theory of oscillations and waves is closest to mathematics. In this book we call the reader's attention to the present-day theory of non-linear oscillations and waves. Oscillatory and wave processes in the systems of diversified physical natures, both periodic and chaotic, are considered from a unified poin t of view . The relation between the theory of oscillations and waves, non-linear dynamics and synergetics is discussed. One of the purposes of this book is to convince reader of the necessity of a thorough study popular branches of of the theory of oscillat ions and waves, and to show that such science as non-linear dynamics, synergetics, soliton theory, and so on, are, in fact , constituent parts of this theory. The primary audiences for this book are researchers having to do with oscillatory and wave processes, and both students and post-graduate students interested in a deep study of the general laws and applications of the theory of oscillations and waves.
Book Synopsis Nonlinear Dynamics by : Muthusamy Lakshmanan
Download or read book Nonlinear Dynamics written by Muthusamy Lakshmanan and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained treatment covers all aspects of nonlinear dynamics, from fundamentals to recent developments, in a unified and comprehensive way. Numerous examples and exercises will help the student to assimilate and apply the techniques presented.
Book Synopsis Exact Controllability and Stabilization of the Wave Equation by : Enrique Zuazua
Download or read book Exact Controllability and Stabilization of the Wave Equation written by Enrique Zuazua and published by Springer Nature. This book was released on with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Exact Controllability and Stabilization by : V. Komornik
Download or read book Exact Controllability and Stabilization written by V. Komornik and published by Elsevier Masson. This book was released on 1994 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Acoustics & Vibration of Mechanical Structures by : Nicolae Herisanu
Download or read book Acoustics & Vibration of Mechanical Structures written by Nicolae Herisanu and published by Trans Tech Publications Ltd. This book was released on 2013-09-27 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Selected, peer reviewed papers from the XII-th International Symposium Acoustics & Vibration of Mechanical Structures (AVMS 2013), May 23-24, 2013, Timişoara, Romania
Book Synopsis Handbook of Mathematical Fluid Dynamics by : S. Friedlander
Download or read book Handbook of Mathematical Fluid Dynamics written by S. Friedlander and published by Elsevier. This book was released on 2002-07-09 with total page 829 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Mathematical Fluid Dynamics is a compendium of essays that provides a survey of the major topics in the subject. Each article traces developments, surveys the results of the past decade, discusses the current state of knowledge and presents major future directions and open problems. Extensive bibliographic material is provided. The book is intended to be useful both to experts in the field and to mathematicians and other scientists who wish to learn about or begin research in mathematical fluid dynamics. The Handbook illuminates an exciting subject that involves rigorous mathematical theory applied to an important physical problem, namely the motion of fluids.
Book Synopsis Directions in Partial Differential Equations by : Michael G. Crandall
Download or read book Directions in Partial Differential Equations written by Michael G. Crandall and published by Academic Press. This book was released on 2014-05-10 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Directions in Partial Differential Equations covers the proceedings of the 1985 Symposium by the same title, conducted by the Mathematics Research Center, held at the University of Wisconsin, Madison. This book is composed of 13 chapters and begins with reviews of the calculus of variations and differential geometry. The subsequent chapters deal with the study of development of singularities, regularity theory, hydrodynamics, mathematical physics, asymptotic behavior, and critical point theory. Other chapters discuss the use of probabilistic methods, the modern theory of Hamilton-Jacobi equations, the interaction between theory and numerical methods for partial differential equations. The remaining chapters explore attempts to understand oscillatory phenomena in solutions of nonlinear equations. This book will be of great value to mathematicians and engineers.
Book Synopsis Wave Propagation in Drilling, Well Logging and Reservoir Applications by : Wilson C. Chin
Download or read book Wave Propagation in Drilling, Well Logging and Reservoir Applications written by Wilson C. Chin and published by John Wiley & Sons. This book was released on 2014-09-19 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wave propagation is central to all areas of petroleum engineering, e.g., drilling vibrations, MWD mud pulse telemetry, swab-surge, geophysical ray tracing, ocean and current interactions, electromagnetic wave and sonic applications in the borehole, but rarely treated rigorously or described in truly scientific terms, even for a single discipline. Wilson Chin, an MIT and Caltech educated scientist who has consulted internationally, provides an integrated, comprehensive, yet readable exposition covering all of the cited topics, offering insights, algorithms and validated methods never before published. A must on every petroleum engineering bookshelf! In particular, the book: Delivers drillstring vibrations models coupling axial, torsional and lateral motions that predict rate-of-penetration, bit bounce and stick-slip as they depend on rock-bit interaction and bottomhole assembly properties, Explains why catastrophic lateral vibrations at the neutral point cannot be observed from the surface even in vertical wells, but providing a proven method to avoid them, Demonstrates why Fermat's "principle of least time" (used in geophysics) applies to non-dissipative media only, but using the "kinematic wave theory" developed at MIT, derives powerful methods applicable to general attenuative inhomogeneous media, Develops new approaches to mud acoustics and applying them to MWD telemetry modeling and strong transients in modern swab-surge applicagtions, Derives new algorithms for borehole geophysics interpretation, e.g., Rh and Rv in electromagnetic wave and permeability in Stoneley waveform analysis, and Outlines many more applications, e.g., wave loadings on offshore platforms, classical problems in wave propagation, and extensions to modern kinematic wave theory. These disciplines, important to all field-oriented activities, are not treated as finite element applications that are simply gridded, "number-crunched" and displayed, but as scientific disciplines deserving of clear explanation. General results are carefully motivated, derived and applied to real-world problems, with results demonstrating the importance and predictive capabilities of the new methods.
Book Synopsis The Physics of Musical Instruments by : Neville H. Fletcher
Download or read book The Physics of Musical Instruments written by Neville H. Fletcher and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 629 pages. Available in PDF, EPUB and Kindle. Book excerpt: The history of musical instruments is nearly as old as the history of civilization itself, and the aesthetic principles upon which judgments of musical quality are based are intimately connected with the whole culture within which the instruments have evolved. An educated modem Western player or listener can make critical judgments about particular instruments or particular per formances but, to be valid, those judgments must be made within the appro priate cultural context. The compass of our book is much less sweeping than the first paragraph might imply, and indeed our discussion is primarily confined to Western musical instruments in current use, but even here we must take account of centuries of tradition. A musical instrument is designed and built for the playing of music of a particular type and, conversely, music is written to be performed on particular instruments. There is no such thing as an "ideal" instrument, even in concept, and indeed the unbounded possibilities of modem digital sound-synthesis really require the composer or performer to define a whole set of instruments if the result is to have any musical coherence. Thus, for example, the sound and response of a violin are judged against a mental image of a perfect violin built up from experience of violins playing music written for them over the centuries. A new instrument may be richer in sound quality and superior in responsiveness, but if it does not fit that image then it is not a better violin.
Book Synopsis Lectures on Nonlinear Evolution Equations by : Reinhard Racke
Download or read book Lectures on Nonlinear Evolution Equations written by Reinhard Racke and published by Birkhäuser. This book was released on 2015-08-31 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book mainly serves as an elementary, self-contained introduction to several important aspects of the theory of global solutions to initial value problems for nonlinear evolution equations. The book employs the classical method of continuation of local solutions with the help of a priori estimates obtained for small data. The existence and uniqueness of small, smooth solutions that are defined for all values of the time parameter are investigated. Moreover, the asymptotic behaviour of the solutions is described as time tends to infinity. The methods for nonlinear wave equations are discussed in detail. Other examples include the equations of elasticity, heat equations, the equations of thermoelasticity, Schrödinger equations, Klein-Gordon equations, Maxwell equations and plate equations. To emphasize the importance of studying the conditions under which small data problems offer global solutions, some blow-up results are briefly described. Moreover, the prospects for corresponding initial boundary value problems and for open questions are provided. In this second edition, initial-boundary value problems in waveguides are additionally considered.
