Analytical Routes to Chaos in Nonlinear Engineering (eBook)

Albert C. J. Luo (Autor)

eBook Download: PDF

2014
John Wiley & Sons (Verlag)
978-1-118-88391-4 (ISBN)

Infos

Nonlinear problems are of interest to engineers, physicists and mathematicians and many other scientists because most systems are inherently nonlinear in nature. As nonlinear equations are difficult to solve, nonlinear systems are commonly approximated by linear equations. This works well up to some accuracy and some range for the input values, but some interesting phenomena such as chaos and singularities are hidden by linearization and perturbation analysis. It follows that some aspects of the behavior of a nonlinear system appear commonly to be chaotic, unpredictable or counterintuitive. Although such a chaotic behavior may resemble a random behavior, it is absolutely deterministic.

Analytical Routes to Chaos in Nonlinear Engineering discusses analytical solutions of periodic motions to chaos or quasi-periodic motions in nonlinear dynamical systems in engineering and considers engineering applications, design, and control. It systematically discusses complex nonlinear phenomena in engineering nonlinear systems, including the periodically forced Duffing oscillator, nonlinear self-excited systems, nonlinear parametric systems and nonlinear rotor systems. Nonlinear models used in engineering are also presented and a brief history of the topic is provided.

Key features:

• Considers engineering applications, design and control
• Presents analytical techniques to show how to find the periodic motions to chaos in nonlinear dynamical systems
• Systematically discusses complex nonlinear phenomena in engineering nonlinear systems
• Presents extensively used nonlinear models in engineering

Analytical Routes to Chaos in Nonlinear Engineering is a practical reference for researchers and practitioners across engineering, mathematics and physics disciplines, and is also a useful source of information for graduate and senior undergraduate students in these areas.

Professor Luo is currently a Distinguished Research Professor at Southern Illinois University Edwardsville. He is an international renowned figure in the area of nonlinear dynamics and mechanics. For about 30 years, Dr. Luo's contributions on nonlinear dynamical systems and mechanics lie in (i) the local singularity theory for discontinuous dynamical systems, (ii) Dynamical systems synchronization, (iii) Analytical solutions of periodic and chaotic motions in nonlinear dynamical systems, (iv) The theory for stochastic and resonant layer in nonlinear Hamiltonian systems, (v) The full nonlinear theory for a deformable body. Such contributions have been scattered into 13 monographs and over 200 peer-reviewed journal and conference papers. His new research results are changing the traditional thinking in nonlinear physics and mathematics. Dr. Luo has served as an editor for the Journal 'Communications in Nonlinear Science and Numerical simulation', book series on Nonlinear Physical Science (HEP) and Nonlinear Systems and Complexity (Springer). Dr. Luo is the editorial member for two journals (i.e., IMeCh E Part K Journal of Multibody Dynamics and Journal of Vibration and Control). He also organized over 30 international symposiums and conferences on Dynamics and Control.

Inhalt

Cover 1
Title Page 5
Copyright 6
Contents 9
Preface 11
Chapter 1 Introduction 13
1.1 Analytical Methods 13
1.1.1 Lagrange Standard Form 13
1.1.2 Perturbation Methods 14
1.1.3 Method of Averaging 17
1.1.4 Generalized Harmonic Balance 20
1.2 Book Layout 36
Chapter 2 Bifurcation Trees in Duffing Oscillators 37
2.1 Analytical Solutions 37
2.2 Period-1 Motions to Chaos 44
2.2.1 Period-1 Motions 45
2.2.2 Period-1 to Period-4 Motions 47
2.2.3 Numerical Simulations 64
2.3 Period-3 Motions to Chaos 69
2.3.1 Independent, Symmetric Period-3 Motions 69
2.3.2 Asymmetric Period-3 Motions 76
2.3.3 Period-3 to Period-6 Motions 83
2.3.4 Numerical Illustrations 94
Chapter 3 Self-Excited Nonlinear Oscillators 99
3.1 van del Pol Oscillators 99
3.1.1 Analytical Solutions 99
3.1.2 Frequency-Amplitude Characteristics 109
3.1.3 Numerical Illustrations 122
3.2 van del Pol-Duffing Oscillators 126
3.2.1 Finite Fourier Series Solutions 126
3.2.2 Analytical Predictions 142
3.2.3 Numerical Illustrations 155
Chapter 4 Parametric Nonlinear Oscillators 163
4.1 Parametric, Quadratic Nonlinear Oscillators 163
4.1.1 Analytical Solutions 163
4.1.2 Analytical Routes to Chaos 168
4.1.3 Numerical Simulations 181
4.2 Parametric Duffing Oscillators 198
4.2.1 Formulations 198
4.2.2 Parametric Hardening Duffing Oscillators 206
Chapter 5 Nonlinear Jeffcott Rotor Systems 221
5.1 Analytical Periodic Motions 221
5.2 Frequency-Amplitude Characteristics 237
5.2.1 Period-1 Motions 238
5.2.2 Analytical Bifurcation Trees 243
5.2.3 Independent Period-5 Motion 251
5.3 Numerical Simulations 258
References 273
Index 277

Produkt-Details

• Erscheint lt. Verlag: 21.4.2014
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Mechanik
• Themenwelt: Technik ► Maschinenbau
• Schlagworte: accuracy • appear • Aspects • Chaos • Chaos / Fractal / Dynamical Systems • Chaos, Fraktale u. dynamische Systeme • commonly • Control Process & Measurements • difficult • Equations • inherently • input values • Interest • interesting • Linear • Linearization • Maschinenbau • Mathematics • Mathematik • mechanical engineering • Mess- u. Regeltechnik • Nature • Nichtlineares System • Nichtlineare u. komplexe Systeme • Nonlinear • Nonlinear and Complex Systems • Nonlinear Equations • Nonlinear problems • Phenomena • Physics • Physik • Range • scientists • Systems
• ISBN-10: 1-118-88391-8 / 1118883918
• ISBN-13: 978-1-118-88391-4 / 9781118883914