The Matrix Analysis of Vibration
The Matrix Analysis of Vibration

Author: R. E. D. Bishop

Publisher: Cambridge University Press

Published: 2008-11-24

Total Pages: 0

ISBN-13: 9780521098854

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Vibration problems arise in the design of almost all engineering machinery and structures. Many of these problems are extremely complex but their solution is essential if a safe and satisfactory design is to be achieved. The equations of motion are often insoluble by the classical methods of the calculus and so it is necessary to approximate on order to reduce them to a set of linear equations. The use of matrices simplifies the solution of sets of linear equations. This book describes the matrix formulation of the equations of motion and techniques for the solution of matrix equations. The book describes some typical computer methods and also includes a large number of problems (with solutions) which may conveniently be solved by using a desk calculating machine.

Matrix Computer Methods of Vibration Analysis
Matrix Computer Methods of Vibration Analysis

Author: D. J. Hatter

Publisher: Butterworth-Heinemann

Published: 2014-05-20

Total Pages: 215

ISBN-13: 1483161544

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Matrix Computer Methods of Vibration Analysis is an eight-chapter introductory text to a particular technique that combines vibration analysis, matrix algebra, and computational methods. This book is emerged from a series of lectures presented at the North-East London Polytechnic. Chapters 1 and 2 introduce the basic concepts of matrix algebra, followed by a discussion on the facilities and methods of use of the computer in Chapter 3. Chapter 4 deals with the synthesis and manipulation of the system matrix for a vibrating system consisting of a number of lumped parameters, each of these being either a point mass or a massless spring. Chapter 5 describes the concept of separate matrices for the stiffnesses and masses of beams or shafts, while Chapter 6 evaluate the systems subjected to forced vibration due to varying frequencies of excitation and damping. Chapters 7 considers the different types of element that can be encountered in the analysis of a shaft or beam for natural frequencies, with an emphasis on the algorithm for dealing with massless shaft elements and point masses. Chapter 8 covers the analysis and computational requirements of torsional vibration. This work is an invaluable source for mathematicians and computer programmers and researchers.

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.

Solving Vibration Analysis Problems Using MATLAB
Solving Vibration Analysis Problems Using MATLAB

Author: Rao V. Dukkipati

Publisher: New Age International

Published: 2007

Total Pages: 14

ISBN-13: 8122420648

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Solving Engineering Vibration Analysis Problems using MATLAB book is designed as an introductory undergraduate or graduate course for engineering students of all disciplines. Vibration analysis is a multidisciplinary subject and presents a system dynamics methodology based on mathematical fundamentals and stresses physical system modeling. The classical methods of vibration analysis engineering are covered: matrix analysis, Laplace transforms and transfer functions. The numerous worked examples and unsolved exercise problems are intended to provide the reader with an awareness of the general applicability of vibration analysis problems using MATLAB. An extensive bibliography to guide the student to further sources of information on vibration analysis using MATLAB is provided at the end of the book. All end-of chapter problems are fully solved in the Solution Manual available only to Instructors.

Lambda-matrices and Vibrating Systems
Lambda-matrices and Vibrating Systems

Author: Peter Lancaster

Publisher: Courier Corporation

Published: 2002-01-01

Total Pages: 226

ISBN-13: 9780486425467

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This text covers several aspects and solutions of the problems of linear vibrating systems with a finite number of degrees of freedom. It offers a detailed account of the part of the theory of matrices necessary for efficient problem-solving, beginning with a focus on developing the necessary tools in matrix theory in the first four chapters. The following chapters present numerical procedures for the relevant matrix formulations and the relevant theory of differential equations. Directed toward a wide audience of applied mathematicians, scientists, and engineers, this book has much to offer all those interested in problem-solving from both practical and theoretical points of view. The mathematically sound treatment involves readers in a minimum of mathematical abstraction; it assumes a familiarity and facility with matrix theory, along with a knowledge of elementary calculus (including the rudiments of the theory of functions of a complex variable). Those already engaged in the practical analysis of vibrating systems have the option of proceeding directly to the more applications-oriented material, starting with Chapter 7; however, this comprehensive treatment offers ample background in the early chapters for less experienced readers. New Preface to the Dover Edition. Errata List. Preface. Bibliographical Notes. References. Index.

Mechanical Vibration
Mechanical Vibration

Author: Haym Benaroya

Publisher: CRC Press

Published: 2017-08-29

Total Pages: 602

ISBN-13: 1498753019

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Mechanical Vibration: Analysis, Uncertainties, and Control, Fourth Edition addresses the principles and application of vibration theory. Equations for modeling vibrating systems are explained, and MATLAB® is referenced as an analysis tool. The Fourth Edition adds more coverage of damping, new case studies, and development of the control aspects in vibration analysis. A MATLAB appendix has also been added to help students with computational analysis. This work includes example problems and explanatory figures, biographies of renowned contributors, and access to a website providing supplementary resources.

Vibration Theory and Applications with Finite Elements and Active Vibration Control
Vibration Theory and Applications with Finite Elements and Active Vibration Control

Author: Alan Palazzolo

Publisher: John Wiley & Sons

Published: 2016-01-11

Total Pages: 973

ISBN-13: 1118404254

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Based on many years of research and teaching, this book brings together all the important topics in linear vibration theory, including failure models, kinematics and modeling, unstable vibrating systems, rotordynamics, model reduction methods, and finite element methods utilizing truss, beam, membrane and solid elements. It also explores in detail active vibration control, instability and modal analysis. The book provides the modeling skills and knowledge required for modern engineering practice, plus the tools needed to identify, formulate and solve engineering problems effectively.

Noise and Vibration Analysis
Noise and Vibration Analysis

Author: Anders Brandt

Publisher: John Wiley & Sons

Published: 2011-03-29

Total Pages: 481

ISBN-13: 0470978112

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Noise and Vibration Analysis is a complete and practical guide that combines both signal processing and modal analysis theory with their practical application in noise and vibration analysis. It provides an invaluable, integrated guide for practicing engineers as well as a suitable introduction for students new to the topic of noise and vibration. Taking a practical learning approach, Brandt includes exercises that allow the content to be developed in an academic course framework or as supplementary material for private and further study. Addresses the theory and application of signal analysis procedures as they are applied in modern instruments and software for noise and vibration analysis Features numerous line diagrams and illustrations Accompanied by a web site at www.wiley.com/go/brandt with numerous MATLAB tools and examples. Noise and Vibration Analysis provides an excellent resource for researchers and engineers from automotive, aerospace, mechanical, or electronics industries who work with experimental or analytical vibration analysis and/or acoustics. It will also appeal to graduate students enrolled in vibration analysis, experimental structural dynamics, or applied signal analysis courses.