Inverse problems in vibration
Inverse problems in vibration

Author: G.M.L. Gladwell

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 272

ISBN-13: 9401511780

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The last thing one settles in writing a book is what one should put in first. Pascal's Pensees Classical vibration theory is concerned, in large part, with the infinitesimal (i. e. , linear) undamped free vibration of various discrete or continuous bodies. One of the basic problems in this theory is the determination of the natural frequencies (eigen frequencies or simply eigenvalues) and normal modes of the vibrating body. A body which is modelled as a discrete system' of rigid masses, rigid rods, massless springs, etc. , will be governed by an ordinary matrix differential equation in time t. It will have a finite number of eigenvalues, and the normal modes will be vectors, called eigenvectors. A body which is modelled as a continuous system will be governed by a partial differential equation in time and one or more spatial variables. It will have an infinite number of eigenvalues, and the normal modes will be functions (eigen functions) of the space variables. In the context of this classical theory, inverse problems are concerned with the construction of a model of a given type; e. g. , a mass-spring system, a string, etc. , which has given eigenvalues and/or eigenvectors or eigenfunctions; i. e. , given spec tral data. In general, if some such spectral data is given, there can be no system, a unique system, or many systems, having these properties.

An Introduction To Inverse Problems In Physics
An Introduction To Inverse Problems In Physics

Author: Mohsen Razavy

Publisher: World Scientific

Published: 2020-05-21

Total Pages: 387

ISBN-13: 9811221685

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This book is a compilation of different methods of formulating and solving inverse problems in physics from classical mechanics to the potentials and nucleus-nucleus scattering. Mathematical proofs are omitted since excellent monographs already exist dealing with these aspects of the inverse problems.The emphasis here is on finding numerical solutions to complicated equations. A detailed discussion is presented on the use of continued fractional expansion, its power and its limitation as applied to various physical problems. In particular, the inverse problem for discrete form of the wave equation is given a detailed exposition and applied to atomic and nuclear scattering, in the latter for elastic as well as inelastic collision. This technique is also used for inverse problem of geomagnetic induction and one-dimensional electrical conductivity. Among other topics covered are the inverse problem of torsional vibration, and also a chapter on the determination of the motion of a body with reflecting surface from its reflection coefficient.

Inverse Problems in Wave Propagation
Inverse Problems in Wave Propagation

Author: Guy Chavent

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 502

ISBN-13: 1461218780

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Inverse problems in wave propagation occur in geophysics, ocean acoustics, civil and environmental engineering, ultrasonic non-destructive testing, biomedical ultrasonics, radar, astrophysics, as well as other areas of science and technology. The papers in this volume cover these scientific and technical topics, together with fundamental mathematical investigations of the relation between waves and scatterers.

Inverse Problems of Vibrational Spectroscopy
Inverse Problems of Vibrational Spectroscopy

Author: I. V. Kochikov

Publisher: VSP

Published: 1999

Total Pages: 316

ISBN-13: 9789067643047

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The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.

Introduction to Inverse Problems for Differential Equations
Introduction to Inverse Problems for Differential Equations

Author: Alemdar Hasanov Hasanoğlu

Publisher: Springer

Published: 2017-07-31

Total Pages: 264

ISBN-13: 331962797X

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This book presents a systematic exposition of the main ideas and methods in treating inverse problems for PDEs arising in basic mathematical models, though it makes no claim to being exhaustive. Mathematical models of most physical phenomena are governed by initial and boundary value problems for PDEs, and inverse problems governed by these equations arise naturally in nearly all branches of science and engineering. The book’s content, especially in the Introduction and Part I, is self-contained and is intended to also be accessible for beginning graduate students, whose mathematical background includes only basic courses in advanced calculus, PDEs and functional analysis. Further, the book can be used as the backbone for a lecture course on inverse and ill-posed problems for partial differential equations. In turn, the second part of the book consists of six nearly-independent chapters. The choice of these chapters was motivated by the fact that the inverse coefficient and source problems considered here are based on the basic and commonly used mathematical models governed by PDEs. These chapters describe not only these inverse problems, but also main inversion methods and techniques. Since the most distinctive features of any inverse problems related to PDEs are hidden in the properties of the corresponding solutions to direct problems, special attention is paid to the investigation of these properties.

Methods of Inverse Problems in Physics
Methods of Inverse Problems in Physics

Author: Dilip N. Ghosh Roy

Publisher: CRC Press

Published: 1991-03-14

Total Pages: 506

ISBN-13: 9780849362583

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This interesting volume focuses on the second of the two broad categories into which problems of physical sciences fall-direct (or forward) and inverse (or backward) problems. It emphasizes one-dimensional problems because of their mathematical clarity. The unique feature of the monograph is its rigorous presentation of inverse problems (from quantum scattering to vibrational systems), transmission lines, and imaging sciences in a single volume. It includes exhaustive discussions on spectral function, inverse scattering integral equations of Gel'fand-Levitan and Marcenko, Povzner-Levitan and Levin transforms, Møller wave operators and Krein's functionals, S-matrix and scattering data, and inverse scattering transform for solving nonlinear evolution equations via inverse solving of a linear, isospectral Schrodinger equation and multisoliton solutions of the K-dV equation, which are of special interest to quantum physicists and mathematicians. The book also gives an exhaustive account of inverse problems in discrete systems, including inverting a Jacobi and a Toeplitz matrix, which can be applied to geophysics, electrical engineering, applied mechanics, and mathematics. A rigorous inverse problem for a continuous transmission line developed by Brown and Wilcox is included. The book concludes with inverse problems in integral geometry, specifically Radon's transform and its inversion, which is of particular interest to imaging scientists. This fascinating volume will interest anyone involved with quantum scattering, theoretical physics, linear and nonlinear optics, geosciences, mechanical, biomedical, and electrical engineering, and imaging research.

Dynamical Inverse Problems: Theory and Application
Dynamical Inverse Problems: Theory and Application

Author: Graham M. L. Gladwell

Publisher: Springer Science & Business Media

Published: 2011-05-25

Total Pages: 229

ISBN-13: 3709106966

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The papers in this volume present an overview of the general aspects and practical applications of dynamic inverse methods, through the interaction of several topics, ranging from classical and advanced inverse problems in vibration, isospectral systems, dynamic methods for structural identification, active vibration control and damage detection, imaging shear stiffness in biological tissues, wave propagation, to computational and experimental aspects relevant for engineering problems.

Vibration Problems in Machines
Vibration Problems in Machines

Author: Arthur W. Lees

Publisher: CRC Press

Published: 2020-07-02

Total Pages: 362

ISBN-13: 1000065901

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Vibration Problems in Machines explains how to infer information about the internal operations of rotating machines from external measurements through methods used to resolve practical plant problems. Second edition includes summary of instrumentation, methods for establishing machine rundown data, relationship between the rundown curves and the ideal frequency response function. The section on balancing has been expanded and examples are given on the strategies for balancing a rotor with a bend, with new section on instabilities. It includes case studies with real plant data, MATLAB® scripts and functions for the modelling and analysis of rotating machines.

Inverse Eigenvalue Problems
Inverse Eigenvalue Problems

Author: Moody Chu

Publisher: Oxford University Press

Published: 2005-06-16

Total Pages: 408

ISBN-13: 0198566646

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Inverse eigenvalue problems arise in a remarkable variety of applications and associated with any inverse eigenvalue problem are two fundamental questions--the theoretical issue of solvability and the practical issue of computability. Both questions are difficult and challenging. In this text, the authors discuss the fundamental questions, some known results, many applications, mathematical properties, a variety of numerical techniques, as well as several open problems.This is the first book in the authoritative Numerical Mathematics and Scientific Computation series to cover numerical linear algebra, a broad area of numerical analysis. Authored by two world-renowned researchers, the book is aimed at graduates and researchers in applied mathematics, engineering and computer science and makes an ideal graduate text.