124,99 €
Mehr erfahren.
- Herausgeber: Wiley-VCH
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
In this introductory treatment Ali Nayfeh presents different concepts from dynamical systems theory and nonlinear dynamics in a rigorous yet plan way. He systematically introduces models and techniques and states the relevant ranges of validity and applicability.
The reader is provided with a clear operational framework for consciously use rather than focused on the underlying mathematical apparatus. The exposition is largely by means of examples, dealt with up to their final outcome. For most of the examples, the results obtained with the method of normal forms are equivalent to those obtained with other perturbation methods, such as the method of multiple scales and the method of averaging.
The previous edition had a remarkable success by researchers from all over the world working in the area of nonlinear dynamics and their applications in engineering. Additions to this new edition concern major topics of current interest. In particular, the author added three new chapters dedicated to Maps, Bifurcations of Continuous Systems, and Retarded Systems. In particular the latter has become of major importance in several applications, both in mechanics and in different areas.
Accessible to engineers and applied scientist involved with nonlinear dynamics and their applications in a wide variety of fields. It is assumed that readers have a knowledge of basic calculus as well as the elementary properties of ordinary-differential equations.
Sie lesen das E-Book in den Legimi-Apps auf:
Seitenzahl: 328
Veröffentlichungsjahr: 2011
Ähnliche
Contents
Cover
Half Title page
Related Titles
Title page
Copyright page
Dedication
Preface
Introduction
Chapter 1: SDOF Autonomous Systems
1.1 Introduction
1.2 Duffing Equation
1.3 Rayleigh Equation
1.4 Duffing–Rayleigh–van der Pol Equation
1.5 An Oscillator with Quadratic and Cubic Nonlinearities
1.6 A General System with Quadratic and Cubic Nonlinearities
1.7 The van der Pol Oscillator
1.8 Exercises
Chapter 2: Systems of First-Order Equations
2.1 Introduction
2.2 A Two-Dimensional System with Diagonal Linear Part
2.3 A Two-Dimensional System with a Nonsemisimple Linear Form
2.4 An n-Dimensional System with Diagonal Linear Part
2.5 A Two-Dimensional System with Purely Imaginary Eigenvalues
2.6 A Two-Dimensional System with Zero Eigenvalues
2.7 A Three-Dimensional System with Zero and Two Purely Imaginary Eigenvalues
2.8 The Mathieu Equation
2.9 Exercises
Chapter 3: Maps
3.1 Linear Maps
3.2 Nonlinear Maps
3.3 Center-Manifold Reduction
3.4 Local Bifurcations
3.5 Exercises
Chapter 4: Bifurcations of Continuous Systems
4.1 Linear Systems
4.2 Fixed Points of Nonlinear Systems
4.3 Center-Manifold Reduction
4.4 Local Bifurcations of Fixed Points
4.5 Normal Forms of Static Bifurcations
4.6 Normal Form of Hopf Bifurcation
4.7 Exercises
Chapter 5: Forced Oscillations of the Duffing Oscillator
5.1 Primary Resonance
5.2 Subharmonic Resonance of Order One-Third
5.3 Superharmonic Resonance of Order Three
5.4 An Alternate Approach
5.5 Exercises
Chapter 6: Forced Oscillations of SDOF Systems
6.1 Introduction
6.2 Primary Resonance
6.3 Subharmonic Resonance of Order One-Half
6.4 Superharmonic Resonance of Order Two
6.5 Subharmonic Resonance of Order One-Third
Chapter 7: Parametrically Excited Systems
7.1 The Mathieu Equation
7.2 Multiple-Degree-of-Freedom Systems
7.3 Linear Systems Having Repeated Frequencies
7.4 Gyroscopic Systems
7.5 A Nonlinear Single-Degree-of-Freedom System
7.6 Exercises
Chapter 8: MDOF Systems with Quadratic Nonlinearities
8.1 Nongyroscopic Systems
8.2 Gyroscopic Systems
8.3 Two Linearly Coupled Oscillators
8.4 Exercises
Chapter 9: TDOF Systems with Cubic Nonlinearities
9.1 Nongyroscopic Systems
9.2 Gyroscopic Systems
Chapter 10: Systems with Quadratic and Cubic Nonlinearities
10.1 Introduction
10.2 The Case of No Internal Resonance
10.3 The Case of Three-to-One Internal Resonance
10.4 The Case of One-to-One Internal Resonance
10.5 The Case of Two-to-One Internal Resonance
10.6 Method of Multiple Scales
10.7 Generalized Method of Averaging
10.8 A Nonsemisimple One-to-One Internal Resonance
10.9 Exercises
Chapter 11: Retarded Systems
11.1 A Scalar Equation
11.2 A Single-Degree-of-Freedom System
11.3 A Three-Dimensional System
11.4 Crane Control with Time-Delayed Feedback
11.5 Exercises
References
Further Reading
Index
Ali Hasan Nayfeh
The Method of Normal Forms
Related Titles
Lalanne, C.Mechanical Vibration and ShockVolume 1: Sinusoidal Vibration2009ISBN 978-1-84821-122-3
Gossett, E.Discrete Mathematics with Proof2009ISBN 978-0-470-45793-1
Talman, R.Geometric MechanicsToward a Unification of Classical Physics2007ISBN 978-3-527-40683-8
Zauderer, E.Partial Differential Equations of Applied Mathematics2006ISBN 978-0-471-69073-3
Kahn, P. B., Zarmi, Y.Nonlinear DynamicsExploration Through Normal Forms1998ISBN 978-0-471-17682-4
Nayfeh, A. H.Introduction to Perturbation Techniques1993ISBN 978-0-471-31013-6
The Author
Prof. Ali Hasan NayfehVirginia Polytechnic Institute and State UniversityDepartment of EngineeringScience and MechanicsBlacksburg, VA 24061USAanayfeh@vt.edu
All books published byWiley-VCH are carefully produced. Nevertheless, authors, editors, and publisher do not warrant the information contained in these books, including this book, to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate.
Library of Congress Card No.: applied for
British Library Cataloguing-in-Publication Data:A catalogue record for this book is available from the British Library.
Bibliographic information published by the Deutsche NationalbibliothekThe Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at http://dnb.d-nb.de.
© 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Boschstr. 12, 69469 Weinheim, Germany
All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form – by photoprinting, microfilm, or any othermeans – nor transmitted or translated into a machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law.
ISBN Print 978-3-527-41097-2
ISBN ePDF 978-3-527-63578-8ISBN oBook 978-3-527-63580-1ISBN ePub 978-3-527-63577-1
To my youngest son Nader
Preface
This book gives an introductory treatment of the method of normal forms. This technique has its application in many branches of engineering, physics, and applied mathematics. Approximation techniques such as these are important for people working with dynamical problems and are a valuable tool they should have in their tool box.
The exposition is largely by means of examples. The readers need not understand the physical bases of the examples used to describe the techniques. However, it is assumed that they have a knowledge of basic calculus as well as the elementary properties of ordinary differential equations. For most of the examples, the results obtained with the method of normal forms are shown to be equivalent to those obtained with other perturbation methods, such as the methods of multiple scales and averaging. As such, new sections are added treating some of the examples with these methods. Moreover, exercises are added to most chapters.
Because the normal forms of maps and differential equations are very useful in bifurcation analysis, I added in this edition three chapters dealing with the normal forms and bifurcations of maps, continuous systems, and retarded systems. The normal forms of continuous systems are constructed using the method of multiple scales, a combination of center-manifold reduction and the method of normal forms, and the new method of projection, which is developed first in this edition. Also, the normal forms of retarded systems are constructed using center-manifold reduction and the method of multiple scales. In the center-manifold reduction, we represent the retarded equations as operator differential equations, decompose the solution space of their linearized form into stable and center subspaces, define an inner product, determine the adjoint of the operator equations, calculate the center manifold, carry out details of the projection using the adjoint of the center subspace, and finally calculate the normal form on the center manifold.
I am very much indebted to my late parents, Hasan and Khadrah, who in spite of their lack of formal education insisted that all their sons obtain the highest degrees. If it were not for their incredible foresight on the value of an education even under the most severe conditions, I would not have finished secondary school. This book and its second edition would not have been written without the patience and continuous encouragement of my wife, Samirah.
Blacksburg, VA, December 2010
Ali Hasan Nayfeh
