INVERSE PROBLEMS IN VIBRATION SOLID MECHANICS AND ITS APPLICATIONS

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Inverse Problems In Vibration

Author : G.M.L. Gladwell
ISBN : 9781402027215
Genre : Technology & Engineering
File Size : 38.44 MB
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In the first, 1986, edition of this book, inverse problems in vibration were interpreted strictly: problems concerning the reconstruction of a unique, undamped vibrating system, of a specified type, from specified vibratory behaviour, particularly specified natural frequencies and/or natural mode shapes. In this new edition the scope of the book has been widened to include topics such as isospectral systems- families of systems which all exhibit some specified behaviour; applications of the concept of Toda flow; new, non-classical approaches to inverse Sturm-Liouville problems; qualitative properties of the modes of some finite element models; damage identification. With its emphasis on analysis, on qualitative results, rather than on computation, the book will appeal to researchers in vibration theory, matrix analysis, differential and integral equations, matrix analysis, non-destructive testing, modal analysis, vibration isolation, etc. "This book is a necessary addition to the library of engineers and mathematicians working in vibration theory." Mathematical Reviews
Category: Technology & Engineering

Inverse Problems In Scattering

Author : G.M.L. Gladwell
ISBN : 9789401120463
Genre : Science
File Size : 58.64 MB
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Inverse Problems in Scattering exposes some of the mathematics which has been developed in attempts to solve the one-dimensional inverse scattering problem. Layered media are treated in Chapters 1--6 and quantum mechanical models in Chapters 7--10. Thus, Chapters 2 and 6 show the connections between matrix theory, Schur's lemma in complex analysis, the Levinson--Durbin algorithm, filter theory, moment problems and orthogonal polynomials. The chapters devoted to the simplest inverse scattering problems in quantum mechanics show how the Gel'fand--Levitan and Marchenko equations arose. The introduction to this problem is an excursion through the inverse problem related to a finite difference version of Schrödinger's equation. One of the basic problems in inverse quantum scattering is to determine what conditions must be imposed on the scattering data to ensure that they correspond to a regular potential, which involves Lebesque integrable functions, which are introduced in Chapter 9.
Category: Science

Foundations Of Solid Mechanics

Author : P. Karasudhi
ISBN : 9789401138147
Genre : Science
File Size : 47.37 MB
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This book has been written with two purposes, as a textbook for engineering courses and as a reference book for engineers and scientists. The book is an outcome of several lecture courses. These include lectures given to graduate students at the Asian Institute of Technology for several years, a course on elasticity for University of Tokyo graduate students in the spring of 1979, and courses on elasticity, viscoelasticity and ftnite deformation at the National University of Singapore from May to November 1985. In preparing this book, I kept three objectives in mind: ftrst, to provide sound fundamental knowledge of solid mechanics in the simplest language possible; second, to introduce effective analytical and numerical solution methods; and third, to impress on readers that the subject is beautiful, and is accessible to those with only a standard mathematical background. In order to meet those objectives, the ftrst chapter of the book is a review of mathematical foundations intended for anyone whose background is an elementary knowledge of differential calculus, scalars and vectors, and Newton's laws of motion. Cartesian tensors are introduced carefully. From then on, only Cartesian tensors in the indicial notation, with subscript as indices, are used to derive and represent all theories.
Category: Science

Inverse Problems In The Mechanics Of Materials

Author : H. D. Bui
ISBN : STANFORD:36105003479115
Genre : Technology & Engineering
File Size : 58.31 MB
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Inverse Problems in the Mechanics of Materials concentrates on two timely subjects: Ill-posed inverse problems related to defect identification; and the mechanics of homogeneous and heterogeneous media, including such topics as cracked bodies, solids with interfaces or inclusions, and materials rendered inhomogeneous by irreversible deformation due to their thermomechanical history. These intriguing subjects are not found together in previous publications. Written in a unique, easy-to-read format, Inverse Problems in the Mechanics of Materials provides quick access to current information. It includes up-to-date references and many recent results, particularly in such classical subjects as elasticity, plasticity, and fracture mechanics. The reader discovers numerous recipes for solving inverse problems, and reviews of available methods provide applications to real-life problems in industry.
Category: Technology & Engineering

Mathematical Reviews

Author :
ISBN : UOM:39015062317220
Genre : Mathematics
File Size : 24.18 MB
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Category: Mathematics

Functional Analysis

Author : L. P. Lebedev
ISBN : 0792338499
Genre : Mathematics
File Size : 67.72 MB
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This is a book for people who want to use functional analysis to justify approximate methods in Mechanics and Inverse Problems. It provides such researchers with the tools they need without having to assimilate or skip through concepts they do not need. The essence of functional analysis is abstraction: from the everyday ideas of 3-dimensional space and distance, one abstracts the concepts of metric space and metric. The properties of this metric are laid down as axioms on which all subsequent arguments are based. The vocabulary of functional analysis consists largely of terms which originally appeared either in geometry or in connection with the real line: set, closed, open, bounded, compact, inner-product, etc.; in functional analysis they are defined abstractly. For the applied mathematician the essential difficulty attending the study of functional analysis is that the pure mathematicians who have developed the field have carried the process of abstraction to increasingly higher levels. In this book the authors have kept the level of abstraction high enough for the majority of applications, and have resisted the temptation to abstract to the limit. The book starts from scratch with a chapter on real numbers and functions. Chapter 2 introduces metric spaces, including the concept of a complete space and Banach's contraction mapping theorem; normed linear spaces, and inner product spaces. An excursion into some boundary value problems in Mechanics leads up to the concept of a generalized solution, and to Sobolev space. A study of approximation in Hilbert space leads to Riesz's representation theorem. An introduction to linear operators is followed by a chapter on the essential, but often misunderstood concept of a compact set. En route the mysteries of weakly closed, weakly convergent, sequential compactness, compact operator, singular value decomposition, etc. are revealed. The final chapter shows how the language of functional analysis is ideally suited to elucidate and justify the regularisation methods for the ill-posed inverse problems exemplified by Fredholm integral equations of the first kind.
Category: Mathematics

Advances In Turbulence V

Author : Roberto Benzi
ISBN : 0792330323
Genre : Mathematics
File Size : 31.58 MB
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Turbulence - the chaotic behaviour of fluid flows - has attracted the interest of many scientists for many decades, and the number is still growing. Turbulence is one of the most challenging classical problems that still require solution. But it is not only a scientific problem: the control of turbulence and turbulent transport are the key to many engineering problems. The Euromech Committee has organised a European Turbulence Conference every two years, starting in 1986, with the 5th Conference in the series taking place in Sienna, Italy, in July 1994. The work presented at this meeting is published in Advances in Turbulence V, providing a complete overview of the most recent research work on the subject.
Category: Mathematics

Introduction To Soliton Theory Applications To Mechanics

Author : Ligia Munteanu
ISBN : 9781402025778
Genre : Mathematics
File Size : 81.14 MB
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This monograph is planned to provide the application of the soliton theory to solve certain practical problems selected from the fields of solid mechanics, fluid mechanics and biomechanics. The work is based mainly on the authors’ research carried out at their home institutes, and on some specified, significant results existing in the published literature. The methodology to study a given evolution equation is to seek the waves of permanent form, to test whether it possesses any symmetry properties, and whether it is stable and solitonic in nature. Students of physics, applied mathematics, and engineering are usually exposed to various branches of nonlinear mechanics, especially to the soliton theory. The soliton is regarded as an entity, a quasi-particle, which conserves its character and interacts with the surroundings and other solitons as a particle. It is related to a strange phenomenon, which consists in the propagation of certain waves without attenuation in dissipative media. This phenomenon has been known for about 200 years (it was described, for example, by the Joule Verne's novel Les histoires de Jean Marie Cabidoulin, Éd. Hetzel), but its detailed quantitative description became possible only in the last 30 years due to the exceptional development of computers. The discovery of the physical soliton is attributed to John Scott Russell. In 1834, Russell was observing a boat being drawn along a narrow channel by a pair of horses.
Category: Mathematics