Mathematical Techniques For Wave Interaction With Flexible Structures

Author : Trilochan Sahoo
Publisher : CRC Press
Page : 244 pages
File Size : 52,8 Mb
Release : 2012-10-24
Category : Technology & Engineering
ISBN : 9781466506046

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Mathematical Techniques for Wave Interaction with Flexible Structures by Trilochan Sahoo Pdf

Mathematical Techniques for Wave Interaction with Flexible Structures is a thoughtful compilation of the various mathematical techniques used to deal with wave structure interaction problems. The book emphasizes unique determination of the solution for a class of physical problems associated with Laplace- or Helmholtz-type equations satisfying higher order boundary conditions with the applications of the theory of ordinary and partial differential equations, Fourier analysis, and more. Features: Provides a focused mathematical treatment for gravity wave interaction with floating and submerged flexible structures Highlights solution methods for a special class of boundary value problems in wave structure interaction Introduces and expands upon differential equations and the fundamentals of wave structure interaction problems This is an ideal handbook for naval architects, ocean engineers, and geophysicists dealing with the design of floating and/or flexible marine structures. The book’s underlying mathematical tools can be easily extended to deal with physical problems in the area of acoustics, electromagnetic waves, wave propagation in elastic media, and solid‐state physics. Designed for both the classroom and independent study, Mathematical Techniques for Wave Interaction with Flexible Structures enables readers to appreciate and apply the mathematical tools of wave structure interaction research to their own work.

Author : C.M. Linton,P. McIver
Publisher : CRC Press
Page : 317 pages
File Size : 49,5 Mb
Release : 2001-02-26
Category : Mathematics
ISBN : 9781420036060

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Handbook of Mathematical Techniques for Wave/Structure Interactions by C.M. Linton,P. McIver Pdf

Although a wide range of mathematical techniques can apply to solving problems involving the interaction of waves with structures, few texts discuss those techniques within that context-most often they are presented without reference to any applications. Handbook of Mathematical Techniques for Wave/Structure Interactions brings together some of the

Author : René Dáger,Enrique Zuazua
Publisher : Springer Science & Business Media
Page : 227 pages
File Size : 49,8 Mb
Release : 2006-08-23
Category : Science
ISBN : 9783540377269

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Wave Propagation, Observation and Control in 1-d Flexible Multi-Structures by René Dáger,Enrique Zuazua Pdf

This book is devoted to analyze the vibrations of simpli?ed 1? d models of multi-body structures consisting of a ?nite number of ?exible strings d- tributed along planar graphs. We?rstdiscussissueson existence and uniquenessof solutions that can be solved by standard methods (energy arguments, semigroup theory, separation ofvariables,transposition,...).Thenweanalyzehowsolutionspropagatealong the graph as the time evolves, addressing the problem of the observation of waves. Roughly, the question of observability can be formulated as follows: Can we obtain complete information on the vibrations by making measu- ments in one single extreme of the network? This formulation is relevant both in the context of control and inverse problems. UsingtheFourierdevelopmentofsolutionsandtechniquesofNonharmonic Fourier Analysis, we give spectral conditions that guarantee the observability property to hold in any time larger than twice the total length of the network in a suitable Hilbert space that can be characterized in terms of Fourier series by means of properly chosen weights. When the network graph is a tree, we characterize these weights in terms of the eigenvalues of the corresponding elliptic problem. The resulting weighted observability inequality allows id- tifying the observable energy in Sobolev terms in some particular cases. That is the case, for instance, when the network is star-shaped and the ratios of the lengths of its strings are algebraic irrational numbers.

Author : Paul A. Milewski
Publisher : American Mathematical Soc.
Page : 132 pages
File Size : 47,8 Mb
Release : 2001-01-01
Category : Mathematics
ISBN : 0821856197

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Advances in Wave Interaction and Turbulence by Paul A. Milewski Pdf

We often think of our natural environment as being composed of very many interacting particles, undergoing individual chaotic motions, of which only very coarse averages are perceptible at scales natural to us. However, we could as well think of the world as being made out of individual waves. This is so not just because the distinction between waves and particles becomes rather blurred at the atomic level, but also because even phenomena at much larger scales are better describedin terms of waves rather than of particles: It is rare in both fluids and solids to observe energy being carried from one region of space to another by a given set of material particles; much more often, this transfer occurs through chains of particles, neither of them moving much, but eachcommunicating with the next, and hence creating these immaterial objects we call waves. Waves occur at many spatial and temporal scales. Many of these waves have small enough amplitude that they can be approximately described by linear theory. However, the joint effect of large sets of waves is governed by nonlinear interactions which are responsible for huge cascades of energy among very disparate scales. Understanding these energy transfers is crucial in order to determine the response oflarge systems, such as the atmosphere and the ocean, to external forcings and dissipation mechanisms which act on scales decades apart. The field of wave turbulence attempts to understand the average behavior of large ensembles of waves, subjected to forcing and dissipation at opposite ends of theirspectrum. It does so by studying individual mechanisms for energy transfer, such as resonant triads and quartets, and attempting to draw from them effects that should not survive averaging. This book presents the proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Dispersive Wave Turbulence held at Mt. Holyoke College (MA). It drew together a group of researchers from many corners of the world, in the context of a perceived renaissance of the field, driven by heated debate aboutthe fundamental mechanism of energy transfer among large sets of waves, as well as by novel applications-and old ones revisited-to the understanding of the natural world. These proceedings reflect the spirit that permeated the conference, that of friendly scientific disagreement and genuine wonderat the rich phenomenology of waves.

Author : B. N. Mandal
Publisher : WIT Press (UK)
Page : 376 pages
File Size : 52,6 Mb
Release : 1997
Category : Fluid mechanics
ISBN : UCSD:31822026145698

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Mathematical Techniques for Water Waves by B. N. Mandal Pdf

The mathematical techniques used to handle various water wave problems are varied and fascinating. This book highlights a number of these techniques in connection with investigations of some classes of water wave problems by leading researchers in this field. The first eight chapters discuss linearised theory while the last two cover nonlinear analysis. This book will be an invaluable source of reference for advanced mathematical work in water wave theory.

Author : René Dáger,Enrique Zuazua
Publisher : Springer
Page : 230 pages
File Size : 53,8 Mb
Release : 2009-09-02
Category : Science
ISBN : 3540812849

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Wave Propagation, Observation and Control in 1-d Flexible Multi-Structures by René Dáger,Enrique Zuazua Pdf

This book is devoted to analyze the vibrations of simpli?ed 1? d models of multi-body structures consisting of a ?nite number of ?exible strings d- tributed along planar graphs. We?rstdiscussissueson existence and uniquenessof solutions that can be solved by standard methods (energy arguments, semigroup theory, separation ofvariables,transposition,...).Thenweanalyzehowsolutionspropagatealong the graph as the time evolves, addressing the problem of the observation of waves. Roughly, the question of observability can be formulated as follows: Can we obtain complete information on the vibrations by making measu- ments in one single extreme of the network? This formulation is relevant both in the context of control and inverse problems. UsingtheFourierdevelopmentofsolutionsandtechniquesofNonharmonic Fourier Analysis, we give spectral conditions that guarantee the observability property to hold in any time larger than twice the total length of the network in a suitable Hilbert space that can be characterized in terms of Fourier series by means of properly chosen weights. When the network graph is a tree, we characterize these weights in terms of the eigenvalues of the corresponding elliptic problem. The resulting weighted observability inequality allows id- tifying the observable energy in Sobolev terms in some particular cases. That is the case, for instance, when the network is star-shaped and the ratios of the lengths of its strings are algebraic irrational numbers.

Author : Nikolaĭ Germanovich Kuznet︠s︡ov,V. G. Mazʹi︠a︡,B. Vainberg
Publisher : Cambridge University Press
Page : 528 pages
File Size : 46,6 Mb
Release : 2002-07-11
Category : Mathematics
ISBN : 0521808537

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Linear Water Waves by Nikolaĭ Germanovich Kuznet︠s︡ov,V. G. Mazʹi︠a︡,B. Vainberg Pdf

This book gives a self-contained and up-to-date account of mathematical results in the linear theory of water waves. The study of waves has many applications, including the prediction of behavior of floating bodies (ships, submarines, tension-leg platforms etc.), the calculation of wave-making resistance in naval architecture, and the description of wave patterns over bottom topography in geophysical hydrodynamics. The first section deals with time-harmonic waves. Three linear boundary value problems serve as the approximate mathematical models for these types of water waves. The next section uses a plethora of mathematical techniques in the investigation of these three problems. The techniques used in the book include integral equations based on Green's functions, various inequalities between the kinetic and potential energy and integral identities which are indispensable for proving the uniqueness theorems. The so-called inverse procedure is applied to constructing examples of non-uniqueness, usually referred to as 'trapped nodes.'

Author : Jan Achenbach
Publisher : Elsevier
Page : 440 pages
File Size : 52,5 Mb
Release : 2012-12-02
Category : Science
ISBN : 9780080934716

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Wave Propagation in Elastic Solids by Jan Achenbach Pdf

The propagation of mechanical disturbances in solids is of interest in many branches of the physical scienses and engineering. This book aims to present an account of the theory of wave propagation in elastic solids. The material is arranged to present an exposition of the basic concepts of mechanical wave propagation within a one-dimensional setting and a discussion of formal aspects of elastodynamic theory in three dimensions, followed by chapters expounding on typical wave propagation phenomena, such as radiation, reflection, refraction, propagation in waveguides, and diffraction. The treatment necessarily involves considerable mathematical analysis. The pertinent mathematical techniques are, however, discussed at some length.

Author : Fernanda Botelho,Thomas Hagen,James E. Jamison
Publisher : American Mathematical Soc.
Page : 300 pages
File Size : 45,8 Mb
Release : 2007-09-19
Category : Mathematics
ISBN : 082185769X

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Fluids and Waves by Fernanda Botelho,Thomas Hagen,James E. Jamison Pdf

This volume contains a series of articles on wave phenomena and fluid dynamics, highlighting recent advances in these two areas of mathematics. The collection is based on lectures presented at the conference ``Fluids and Waves--Recent Trends in Applied Analysis'' and features a rich spectrum of mathematical techniques in analysis and applications to engineering, neuroscience, physics, and biology. The mathematical topics discussed range from partial differential equations, dynamical systems and stochastic processes, to areas of classical analysis. This volume is intended as an introduction to major topics of interest and state-of-the-art analytical research in wave motion and fluid flows. It is helpful to junior mathematicians to stay abreast of new techniques and recent trends in these areas of mathematics. The articles here also provide a unique scientific basis for recent results and new links between current research themes. In summary, this book is a guide for experts in one field to the issues of the other, and will challenge graduate students to investigate these areas of analysis in further detail.

Author : Lui Lam,Hedley C. Morris
Publisher : Springer Science & Business Media
Page : 281 pages
File Size : 53,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461388562

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Wave Phenomena by Lui Lam,Hedley C. Morris Pdf

IJ:1 June of 1987 the Center for Applied Mathematics and Computer Science at San Jose State University received a bequest of over half a million dollars from the estate of Mrs. Marie Woodward. In the opening article of this collection of papers Jane Day, the founder of the Center, describes the background that led to this gift. In recognition of the bequest it was decided that a series of Woodward Conferences be established. The First Woodward Conference took place at San Jose State University on June 2-3 1988. The themes of the conference were the Theoretical, Computational and Practical Aspects of Wave Phenomena and these same themes have been used to divide the contributions to this volume. Part I is concerned with papers on theoretical aspects. This section includes papers on pseudo-differential operator techniques, inverse problems and the mathematical foundations of wave propagation in random media. Part II consists of papers that involve significant amounts of computation. Included are papers on the Fast Hartley Transform, computational algorithms for electromagnetic scattering problems, and nonlinear wave interaction problems in fluid mechanics. vi Part III contains papers with a genuine physics flavor. This final section illustrates the widespread importance of wave phenomena in physics. Among the phenomena considered are waves in the atmosphere, viscous fingering in liquid crystals, solitons and wave localization.

Author : Anonim
Publisher : Unknown
Page : 516 pages
File Size : 46,9 Mb
Release : 1989-07
Category : Science
ISBN : CORNELL:31924057174538

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Technical Reports Awareness Circular : TRAC. by Anonim Pdf

Author : Anonim
Publisher : Unknown
Page : 396 pages
File Size : 43,5 Mb
Release : 1986
Category : Fluid mechanics
ISBN : STANFORD:36105013127910

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Civil Engineering Hydraulics Abstracts by Anonim Pdf

Author : Vassily Babich,Aleksei Kiselev
Publisher : Chapman & Hall/CRC
Page : 286 pages
File Size : 47,9 Mb
Release : 2018
Category : Elastic waves
ISBN : 1138033065

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Elastic Waves by Vassily Babich,Aleksei Kiselev Pdf

Elastic Waves: High Frequency Theory is concerned with mathematical aspects of the theory of high-frequency elastic waves, which is based on the ray method. The foundations of elastodynamics are presented along with the basic theory of plane and spherical waves. The ray method is then described in considerable detail for bulk waves in isotropic and anisotropic media, and also for the Rayleigh waves on the surface of inhomogeneous anisotropic elastic solids. Much attention is paid to analysis of higher-order terms and to generation of waves in inhomogeneous media. The aim of the book is to present a clear, systematic description of the ray method, and at the same time to emphasize its mathematical beauty. Luckily, this beauty is usually not accompanied by complexity and mathematical ornateness.

Author : Anonim
Publisher : Unknown
Page : 1246 pages
File Size : 41,7 Mb
Release : 1998
Category : Research grants
ISBN : UOM:39015053960202

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Directory of Research Grants by Anonim Pdf

Author : Brian Seymour,Michael P. Mortell
Publisher : World Scientific Publishing Company
Page : 405 pages
File Size : 43,9 Mb
Release : 2016-12-29
Category : Technology & Engineering
ISBN : 9813100338

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Nonlinear Waves in Bounded Media by Brian Seymour,Michael P. Mortell Pdf

This unique book aims to treat a class of nonlinear waves that are reflected from the boundaries of media of finite extent. It involves both standing (unforced) waves and resonant oscillations due to external periodic forcing. The waves are both hyperbolic and dispersive. To achieve this aim, the book develops the necessary understanding of linear waves and the mathematical techniques of nonlinear waves before dealing with nonlinear waves in bounded media. The examples used come mainly from gas dynamics, water waves and viscoelastic waves.