Overview

An ideal text for students that ties together classical and modern topics of advanced vibration analysis in an interesting and lucid manner. It provides students with a background in elementary vibrations with the tools necessary for understanding and analyzing more complex dynamical phenomena that can be encountered in engineering and scientific practice. It progresses steadily from linear vibration theory over various levels of nonlinearity to bifurcation analysis, global dynamics and chaotic vibrations. It trains the student to analyze simple models, recognize nonlinear phenomena and work with advanced tools such as perturbation analysis and bifurcation analysis. Explaining theory in terms of relevant examples from real systems, this book is user-friendly and meets the increasing interest in non-linear dynamics in mechanical/structural engineering and applied mathematics and physics. This edition includes a new chapter on the useful effects of fast vibrations and many new exercise problems.

Full Product Details

Author:   Jon Juel Thomsen
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   Softcover reprint of hardcover 2nd ed. 2004
Dimensions:   Width: 15.50cm , Height: 2.20cm , Length: 23.50cm
Weight:   0.652kg
ISBN:  

9783642072727

ISBN 10:   3642072720
Pages:   404
Publication Date:   30 November 2010
Audience:   Professional and scholarly ,  Professional and scholarly ,  Professional & Vocational ,  Postgraduate, Research & Scholarly
Replaced By:   9783030680442
Format:   Paperback
Publisher's Status:   Out of Print
Availability:   Awaiting stock  

Table of Contents

1 Vibration Basics.- 2 Eigenvalue Problems of Vibrations And Stability.- 3 Nonlinear Vibrations: Classical Local Theory.- 4 Nonlinear Multiple-DOF Systems: Local Analysis.- 5 Bifurcations.- 6 Chaotic Vibrations.- 7 Special Effects of High-Frequency Excitation.- Appendix A — Performing Numerical Simulations.- A.1 Solving Differential Equations.- A.2 Computing Chaos-Related Quantities.- A.3 Interfacing with the ODE-Solver.- A.4 Locating Software on the Internet.- Appendix B — Major Exercises.- B.1 Tension Control of Rotating Shafts.- B.1.1 Mathematical Model.- B.1.2 Eigenvalue Problem, Natural Frequencies and Mode Shapes.- B.1.3 Discretisations, Choice of Control Law.- B.1.5 Quantitative Analysis of the Controlled System.- B.1.6 Using a Dither Signal for Open-Loop Control.- B.1.7 Numerical Analysis of the Controlled System.- B.1.8 Conclusions.- B.2 Vibrations of a Spring-Tensioned Beam.- B.2.1 Mathematical Model.- B.2.2 Eigenvalue Problem, Natural Frequencies and Mode Shapes.- B.2.3 Discrete Models.- B.2.4 Local Bifurcation Analysis for the Unloaded System.- B.2.5 Quantitative Analysis of the Loaded System.- B.2.6 Numerical Analysis.- B.2.7 Conclusions.- B.3 Dynamics of a Microbeam.- B.3.1 System Description.- B.3.2 Mathematical Model.- B.3.3 Eigenvalue Problem, Natural Frequencies and Mode Shapes.- B.3.4 Discrete Models, Mode Shape Expansion.- B.3.5 Local Bifurcation Analysis for the Statically Loaded System.- B.3.6 Quantitative Analysis of the Loaded System.- B.3.7 Numerical Analysis.- B.3.8 Conclusions.- Appendix C — Mathematical Formulas.- C.1 Formulas Typically Used in Perturbation analysis.- C.1.1 Complex Numbers.- C.1.2 Powers of Two-Term Sums.- C.1.3 Dirac’s Delta Function (?).- C.1.4 Averaging Integrals.- C.1.5 Fourier Series of a Periodic Function.- C.2 Formulas for Stability Analysis.- C.2.1 The Routh-Hurwitz Criterion.- C.2.2 Mathieu’s Equation:Stability of the Zero-Solution.- Appendix D — Vibration Modes and Frequencies for Structural Elements.- D.1 Rods.- D.1.1 Longitudinal Vibrations.- D.1.2 Torsional Vibrations.- D.2 Beams.- D.2.1 Bernoulli-Euler Theory.- D.2.2 Timoshenko Theory.- D.3 Rings.- D.3.1 In-Plane Bending.- D.3.2 Out-of-Plane Bending.- D.3.3 Extension.- D.4 Membranes.- D.4.1 Rectangular Membrane.- D.4.2 Circular Membrane.- D.5 Plates.- D.5.1 Rectangular Plate.- D.5.2 Circular Plate.- D.6 Other Structures.- Appendix E — Properties of Engineering Materials.- E.1 Friction and Thermal Expansion Coefficients.- E.2 Density and Elasticity Constants.- References.

Reviews

From the reviews of the second edition: Vibrations and stability ! attracted a vast amount of attention of a multitude of researchers in the past and present and will remain highly topical in the future. ! The 2nd edition of the book, a thoroughly revised and expanded version of the 1st edition, is an essential by-product of this evolution. ! In the reviewer's opinion the author ! has written a highly recommendable book. I am very pleased to review the book. ! It presents a very readable and well-structured account ! . (Dr C. B. Sharma, Contemporary Physics, Vol. 45 (6), 2004) The second edition of 'Vibrations and Stability' is an accomplished and valuable book, mainly devoted to vibrations in the non-linear regime. ! It is a pleasure to read this clearly written book, which achieves the aim of presenting important material on non-linear vibrations in a useful and quite understandable manner. ! relevant references are given for readers interested in more information. ! Engineers, researchers, and particularly students and teachers in mechanical and structural engineering will find this to be a very helpful book. (Pedro Ribeiro, Journal of Sound and Vibration, Vol. 274 (4-5), 2004) Every chapter is equipped with useful exercises. The reviewed book will be very useful in engineering and scientific practice. (Boris V. Loginov, Zentralblatt MATH, Vol. 1086, 2006)

From the reviews of the second edition: Vibrations and stability ... attracted a vast amount of attention of a multitude of researchers in the past and present and will remain highly topical in the future. ... The 2nd edition of the book, a thoroughly revised and expanded version of the 1st edition, is an essential by-product of this evolution. ... In the reviewer's opinion the author ... has written a highly recommendable book. I am very pleased to review the book. ... It presents a very readable and well-structured account ... . (Dr C. B. Sharma, Contemporary Physics, Vol. 45 (6), 2004) The second edition of `Vibrations and Stability' is an accomplished and valuable book, mainly devoted to vibrations in the non-linear regime. ... It is a pleasure to read this clearly written book, which achieves the aim of presenting important material on non-linear vibrations in a useful and quite understandable manner. ... relevant references are given for readers interested in more information. ... Engineers, researchers, and particularly students and teachers in mechanical and structural engineering will find this to be a very helpful book. (Pedro Ribeiro, Journal of Sound and Vibration, Vol. 274 (4-5), 2004) Every chapter is equipped with useful exercises. The reviewed book will be very useful in engineering and scientific practice. (Boris V. Loginov, Zentralblatt MATH, Vol. 1086, 2006)

From the reviews of the second edition: Vibrations and stability ... attracted a vast amount of attention of a multitude of researchers in the past and present and will remain highly topical in the future. ... The 2nd edition of the book, a thoroughly revised and expanded version of the 1st edition, is an essential by-product of this evolution. ... In the reviewer's opinion the author ... has written a highly recommendable book. I am very pleased to review the book. ... It presents a very readable and well-structured account ... . (Dr C. B. Sharma, Contemporary Physics, Vol. 45 (6), 2004) The second edition of 'Vibrations and Stability' is an accomplished and valuable book, mainly devoted to vibrations in the non-linear regime. ... It is a pleasure to read this clearly written book, which achieves the aim of presenting important material on non-linear vibrations in a useful and quite understandable manner. ... relevant references are given for readers interested in more information. ... Engineers, researchers, and particularly students and teachers in mechanical and structural engineering will find this to be a very helpful book. (Pedro Ribeiro, Journal of Sound and Vibration, Vol. 274 (4-5), 2004) Every chapter is equipped with useful exercises. The reviewed book will be very useful in engineering and scientific practice. (Boris V. Loginov, Zentralblatt MATH, Vol. 1086, 2006)

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