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 : 44.90 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

Functional Analysis

Author : Leonid P. Lebedev
ISBN : 9780306483974
Genre : Mathematics
File Size : 56.35 MB
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This book started its life as a series of lectures given by the second author from the 1970’s onwards to students in their third and fourth years in the Department of Mechanics and Mathematics at Rostov State University. For these lectures there was also an audience of engineers and applied mechanicists who wished to understand the functional analysis used in contemporary research in their fields. These people were not so much interested in functional analysis itself as in its applications; they did not want to be told about functional analysis in its most abstract form, but wanted a guided tour through those parts of the analysis needed for their applications. The lecture notes evolved over the years as the first author started to make more formal typewritten versions incorporating new material. About 1990 the first author prepared an English version and submitted it to Kluwer Academic Publishers for inclusion in the series Solid Mechanics and its Applications. At that state the notes were divided into three long chapters covering linear and nonlinear analysis. As Series Editor, the third author started to edit them. The requirements of lecture notes and books are vastly different. A book has to be complete (in some sense), self contained, and able to be read without the help of an instructor.
Category: Mathematics

Inverse Problems In Scattering

Author : G.M.L. Gladwell
ISBN : 9789401120463
Genre : Science
File Size : 27.74 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

Inverse Problems In Engineering Mechanics Iii

Author : G.S. Dulikravich
ISBN : 0080535143
Genre : Science
File Size : 66.51 MB
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Inverse Problems are found in many areas of engineering mechanics and there are many successful applications e.g. in non-destructive testing and characterization of material properties by ultrasonic or X-ray techniques, thermography, etc. Generally speaking, inverse problems are concerned with the determination of the input and the characteristics of a system, given certain aspects of its output. Mathematically, such problems are ill-posed and have to be overcome through development of new computational schemes, regularization techniques, objective functionals, and experimental procedures. This volume contains a selection of peer-reviewed papers presented at the International Symposium on Inverse Problems in Engineering Mechanics (ISIP2001), held in February of 2001 in Nagano, Japan, where recent development in inverse problems in engineering mechanics and related topics were discussed. The following general areas in inverse problems in engineering mechanics were the subjects of the ISIP2001: mathematical and computational aspects of inverse problems, parameter or system identification, shape determination, sensitivity analysis, optimization, material property characterization, ultrasonic non-destructive testing, elastodynamic inverse problems, thermal inverse problems, and other engineering applications. These papers can provide a state-of-the-art review of the research on inverse problems in engineering mechanics.
Category: Science

Foundations Of Solid Mechanics

Author : P. Karasudhi
ISBN : 0792307720
Genre : Science
File Size : 53.30 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

Full Field Measurements And Identification In Solid Mechanics

Author : Michel Grediac
ISBN : 9781118578476
Genre : Science
File Size : 81.5 MB
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This timely book presents cutting-edge developments by experts in the field on the rapidly developing and scientifically challenging area of full-field measurement techniques used in solid mechanics – including photoelasticity, grid methods, deflectometry, holography, speckle interferometry and digital image correlation. The evaluation of strains and the use of the measurements in subsequent parameter identification techniques to determine material properties are also presented. Since parametric identification techniques require a close coupling of theoretical models and experimental measurements, the book focuses on specific modeling approaches that include finite element model updating, the equilibrium gap method, constitutive equation gap method, virtual field method and reciprocity gap method. In the latter part of the book, the authors discuss two particular applications of selected methods that are of special interest to many investigators: the analysis of localized phenomenon and connections between microstructure and constitutive laws. The final chapter highlights infrared measurements and their use in the mechanics of materials. Written and edited by knowledgeable scientists, experts in their fields, this book will be a valuable resource for all students, faculties and scientists seeking to expand their understanding of an important, growing research area
Category: Science

Inverse Problems In The Mechanics Of Materials

Author : H. D. Bui
ISBN : STANFORD:36105003479115
Genre : Technology & Engineering
File Size : 74.77 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 : 81.32 MB
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Category: Mathematics

Mechanical Vibrations

Author : Michel Geradin
ISBN : 9781118900208
Genre : Science
File Size : 22.87 MB
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Category: Science

Computational Methods For Inverse Problems

Author : Curtis R. Vogel
ISBN : 9780898717570
Genre : Mathematics
File Size : 90.38 MB
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Provides a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems.
Category: Mathematics