Analytical Routes to Chaos in Nonlinear Engineering.

Format:

Book

Author/Creator:

Luo, Albert C. J.

Language:

English

Subjects (All):

Chaotic behavior in systems.

Nonlinear control theory.

Nonlinear systems.

Systems engineering.

Local Subjects:

Chaotic behavior in systems.

Nonlinear control theory.

Nonlinear systems.

Systems engineering.

Physical Description:

1 online resource (278 p.)

Edition:

1st ed.

Place of Publication:

Hoboken : Wiley, 2014.

Summary:

Comprehensively covers analytical solutions of periodic motions to chaos in nonlinear dynamical systems, considering engineering applications, design and control Analytical Routes to Chaos in Nonlinear Engineering discusses analytical solutions of periodic motions to chaos 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 duffing oscillator, nonlinear self-excited systems, nonlinear parametric systems and nonlin

Contents:

Cover; Title Page; Copyright; Contents; Preface; Chapter 1 Introduction; 1.1 Analytical Methods; 1.1.1 Lagrange Standard Form; 1.1.2 Perturbation Methods; 1.1.3 Method of Averaging; 1.1.4 Generalized Harmonic Balance; 1.2 Book Layout; Chapter 2 Bifurcation Trees in Duffing Oscillators; 2.1 Analytical Solutions; 2.2 Period-1 Motions to Chaos; 2.2.1 Period-1 Motions; 2.2.2 Period-1 to Period-4 Motions; 2.2.3 Numerical Simulations; 2.3 Period-3 Motions to Chaos; 2.3.1 Independent, Symmetric Period-3 Motions; 2.3.2 Asymmetric Period-3 Motions; 2.3.3 Period-3 to Period-6 Motions

2.3.4 Numerical IllustrationsChapter 3 Self-Excited Nonlinear Oscillators; 3.1 van del Pol Oscillators; 3.1.1 Analytical Solutions; 3.1.2 Frequency-Amplitude Characteristics; 3.1.3 Numerical Illustrations; 3.2 van del Pol-Duffing Oscillators; 3.2.1 Finite Fourier Series Solutions; 3.2.2 Analytical Predictions; 3.2.3 Numerical Illustrations; Chapter 4 Parametric Nonlinear Oscillators; 4.1 Parametric, Quadratic Nonlinear Oscillators; 4.1.1 Analytical Solutions; 4.1.2 Analytical Routes to Chaos; 4.1.3 Numerical Simulations; 4.2 Parametric Duffing Oscillators; 4.2.1 Formulations

4.2.2 Parametric Hardening Duffing OscillatorsChapter 5 Nonlinear Jeffcott Rotor Systems; 5.1 Analytical Periodic Motions; 5.2 Frequency-Amplitude Characteristics; 5.2.1 Period-1 Motions; 5.2.2 Analytical Bifurcation Trees; 5.2.3 Independent Period-5 Motion; 5.3 Numerical Simulations; References; Index

Notes:

Description based upon print version of record.

ISBN:

9781118883921

1118883926

9781118883938

1118883934