Isospectral Vibrating Systems

Isospectral Vibrating Systems PDF

Author: Ranjan Ganguli

Publisher: CRC Press

Published: 2021-08-10

Total Pages: 303

ISBN-13: 1000413462

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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

Advances in Engineering Structures, Mechanics & Construction PDF

Author: M. Pandey

Publisher: Springer Science & Business Media

Published: 2007-02-10

Total Pages: 847

ISBN-13: 1402048912

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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.

Operator Theory and Indefinite Inner Product Spaces

Operator Theory and Indefinite Inner Product Spaces PDF

Author: Matthias Langer

Publisher: Springer Science & Business Media

Published: 2006-06-16

Total Pages: 403

ISBN-13: 3764375167

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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.

Modern Practice in Stress and Vibration Analysis

Modern Practice in Stress and Vibration Analysis PDF

Author: Matthew P. Cartmell

Publisher: Trans Tech Publications Ltd

Published: 2003-11-15

Total Pages: 550

ISBN-13: 303570614X

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Volume is indexed by Thomson Reuters CPCI-S (WoS). The trend towards the integration of modeling, analysis and design tools, which began in the 1990s, is now well underway, and it is becoming increasingly evident that formerly disparate engineering functions, such as stress analysis, fracture mechanics, elasticity and vibration analysis, will continue to move closer together, as seamlessly integrated computational design tools evolve. The series of Modern Practice in Stress and Vibration Analysis conferences has always reflected this alliance, with its tradition of encouraging specialist contributions to the development and enhanced application of powerful numerical methods; in conjunction with seminal papers on new techniques in experimental mechanics.

Advances in the Theory of System Decoupling

Advances in the Theory of System Decoupling PDF

Author: Rubens Gonçalves Salsa Junior

Publisher: Springer Nature

Published: 2020-11-21

Total Pages: 164

ISBN-13: 3030608468

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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.

Inverse problems in vibration

Inverse problems in vibration PDF

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.

Dynamical Inverse Problems: Theory and Application

Dynamical Inverse Problems: Theory and Application PDF

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.

Eigenvalues of Inhomogeneous Structures

Eigenvalues of Inhomogeneous Structures PDF

Author: Isaac Elishakoff

Publisher: CRC Press

Published: 2004-10-28

Total Pages: 746

ISBN-13: 142003801X

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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

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