Isospectral Vibrating Systems
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Isospectral Vibrating Systems
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Author : Ranjan Ganguli
language : en
Publisher: CRC Press
Release Date : 2021-08-10
Isospectral Vibrating Systems written by Ranjan Ganguli and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-10 with Mathematics categories.
This book presents an isospectral approach for several important mechanical vibrating systems. Discrete and continuous isospectral systems are discussed using a simple multi-degree of freedom spring-mass system followed by illustration of isospectral beams and their solution through evolutionary computing. Next, it addresses axially loaded Euler-Bernoulli beams and aims to find isospectral counterparts of these systems. The practical application of these isospectral systems for vibration testing and for finding new closed form solutions is discussed. A considerable part of the book is devoted to isospectral rotating beams and their non-rotating analogs including Rayleigh beams. Aimed at researchers and graduate students in mechanical; aerospace; civil; automotive; ocean engineering especially mechanical vibrations, this monograph: Discusses isospectral vibrating systems to aid vibration testing and computational analysis Explores isospectral analogs between rotating and non-rotating structures Provides simpler isospectral beams for vibration testing and for 3D printing Uses firefly optimization method and electromagnetism inspired optimization method to find isospectral systems Shows the use of isospectral systems to find new closed form solutions using an indirect approach
Advances In Engineering Structures Mechanics Construction
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Author : M. Pandey
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-02-10
Advances In Engineering Structures Mechanics Construction written by M. Pandey and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-02-10 with Science categories.
This book presents the proceedings of an International Conference on Advances in Engineering Structures, Mechanics & Construction, held in Waterloo, Ontario, Canada, May 14-17, 2006. The contents include contains the texts of all three plenary presentations and all seventy-three technical papers by more than 153 authors, presenting the latest advances in engineering structures, mechanics and construction research and practice.
Modern Practice In Stress And Vibration Analysis
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Author : Matthew P. Cartmell
language : en
Publisher: Trans Tech Publications Ltd
Release Date : 2003-11-15
Modern Practice In Stress And Vibration Analysis written by Matthew P. Cartmell and has been published by Trans Tech Publications Ltd this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-11-15 with Technology & Engineering categories.
Proceedings of the 5th International Conference on Modern Practice in Stress and Vibration Analysis, Glasgow, Scotland, 9-11 September 2003
Inverse Problems In Vibration
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Author : G.M.L. Gladwell
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Inverse Problems In Vibration written by G.M.L. Gladwell and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.
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.
Operator Theory And Indefinite Inner Product Spaces
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Author : Matthias Langer
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-06-16
Operator Theory And Indefinite Inner Product Spaces written by Matthias Langer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-16 with Mathematics categories.
A colloquium on operator theory was held in Vienna, Austria, in March 2004, on the occasion of the retirement of Heinz Langer, a leading expert in operator theory and indefinite inner product spaces. The book contains fifteen refereed articles reporting on recent and original results in various areas of operator theory, all of them related with the work of Heinz Langer. The topics range from abstract spectral theory in Krein spaces to more concrete applications, such as boundary value problems, the study of orthogonal functions, or moment problems. The book closes with a historical survey paper.
Introduction To Isospectrality
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Author : Alberto Arabia
language : en
Publisher: Springer Nature
Release Date : 2022-09-13
Introduction To Isospectrality written by Alberto Arabia and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-13 with Mathematics categories.
"Can one hear the shape of a drum?" This striking question, made famous by Mark Kac, conceals a precise mathematical problem, whose study led to sophisticated mathematics. This textbook presents the theory underlying the problem, for the first time in a form accessible to students. Specifically, this book provides a detailed presentation of Sunada's method and the construction of non-isometric yet isospectral drum membranes, as first discovered by Gordon–Webb–Wolpert. The book begins with an introductory chapter on Spectral Geometry, emphasizing isospectrality and providing a panoramic view (without proofs) of the Sunada–Bérard–Buser strategy. The rest of the book consists of three chapters. Chapter 2 gives an elementary treatment of flat surfaces and describes Buser's combinatorial method to construct a flat surface with a given group of isometries (a Buser surface). Chapter 3 proves the main isospectrality theorems and describes the transplantation technique on Buser surfaces. Chapter 4 builds Gordon–Webb–Wolpert domains from Buser surfaces and establishes their isospectrality. Richly illustrated and supported by four substantial appendices, this book is suitable for lecture courses to students having completed introductory graduate courses in algebra, analysis, differential geometry and topology. It also offers researchers an elegant, self-contained reference on the topic of isospectrality.
Dynamical Inverse Problems Theory And Application
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Author : Graham M. L. Gladwell
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-05-25
Dynamical Inverse Problems Theory And Application written by Graham M. L. Gladwell and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-05-25 with Technology & Engineering categories.
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.
Eigenvalues Of Inhomogeneous Structures
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Author : Isaac Elishakoff
language : en
Publisher: CRC Press
Release Date : 2004-10-28
Eigenvalues Of Inhomogeneous Structures written by Isaac Elishakoff and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-28 with Science categories.
The engineering community generally accepts that there exists only a small set of closed-form solutions for simple cases of bars, beams, columns, and plates. Despite the advances in powerful computing and advanced numerical techniques, closed-form solutions remain important for engineering; these include uses for preliminary design, for evaluation
Advances In The Theory Of System Decoupling
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Author : Rubens Gonçalves Salsa Junior
language : en
Publisher: Springer Nature
Release Date : 2020-11-21
Advances In The Theory Of System Decoupling written by Rubens Gonçalves Salsa Junior and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-21 with Technology & Engineering categories.
This book presents a concise, clear, and consistent account of the methodology of phase synchronization, an extension of modal analysis to decouple any linear system in real space. It expounds on the novel theory of phase synchronization and presents recent advances, while also providing relevant background on classical decoupling theories that are used in structural analysis. The theory is illustrated with a broad range of examples. The theoretical development is also supplemented by applications to engineering problems. In addition, the methodology is implemented in a MATLAB algorithm which can be used to solve many of the illustrative examples in the book. This book is suited for researchers, practicing engineers, and graduate students in various fields of engineering, mathematics, and physical science.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2008
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.