Ebook: Bifurcation and Chaos in Engineering

For the many different deterministic non-linear dynamic systems (physical, mechanical, technical, chemical, ecological, economic, and civil and structural engineering), the discovery of irregular vibrations in addition to periodic and almost periodic vibrations is one of the most significant achievements of modern science. An in-depth study of the theory and application of non-linear science will certainly change one's perception of numerous non-linear phenomena and laws considerably, together with its great effects on many areas of application. As the important subject matter of non-linear science, bifurcation theory, singularity theory and chaos theory have developed rapidly in the past two or three decades. They are now advancing vigorously in their applications to mathematics, physics, mechanics and many technical areas worldwide, and they will be the main subjects of our concern. This book is concerned with applications of the methods of dynamic systems and subharmonic bifurcation theory in the study of non-linear dynamics in engineering. It has grown out of the class notes for graduate courses on bifurcation theory, chaos and application theory of non-linear dynamic systems, supplemented with our latest results of scientific research and materials from literature in this field. The bifurcation and chaotic vibration of deterministic non-linear dynamic systems are studied from the viewpoint of non-linear vibration.

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This work deals effectively and systematically with the main contents of modern analytical methods of nonlinear science, dynamic systems and the basic concepts of the theory and its applications in engineering. While many books consider systems involving only a few unknowns, a real engineering system involves thousands, and this work emphasises the reduction of the number of these unknowns while capturing the essential physical phenomena. Methods of Liapunov-Schmidt reduction, central manifold, normal form and averaging are discussed in detail. Computational methods for harmonic balance, normal form, symplectic integration and invariant torus are studied. Finally, applications to solid mechanics, rotating shaft, flutter and galloping are given. This book can be used as a textbook or reference guide to the subject by undergraduate and postgraduate students studying in areas such as mechanics, mathematics, physics and a wide range of related scientific disciplines. It will also be valuable as a reference book for teachers, researchers and engineering designers.

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This work deals effectively and systematically with the main contents of modern analytical methods of nonlinear science, dynamic systems and the basic concepts of the theory and its applications in engineering. While many books consider systems involving only a few unknowns, a real engineering system involves thousands, and this work emphasises the reduction of the number of these unknowns while capturing the essential physical phenomena. Methods of Liapunov-Schmidt reduction, central manifold, normal form and averaging are discussed in detail. Computational methods for harmonic balance, normal form, symplectic integration and invariant torus are studied. Finally, applications to solid mechanics, rotating shaft, flutter and galloping are given. This book can be used as a textbook or reference guide to the subject by undergraduate and postgraduate students studying in areas such as mechanics, mathematics, physics and a wide range of related scientific disciplines. It will also be valuable as a reference book for teachers, researchers and engineering designers.
Content:
Front Matter....Pages i-xii
Dynamical Systems, Ordinary Differential Equations and Stability of Motion....Pages 1-34
Calculation of Flows....Pages 35-65
Discrete Dynamical Systems....Pages 66-83
Liapunov—Schmidt Reduction....Pages 84-153
Centre Manifold Theorem and Normal Form Of Vector Fields....Pages 154-175
Hopf Bifurcation....Pages 176-229
Application of the Averaging Method in Bifurcation Theory....Pages 230-264
Brief Introduction to Chaos....Pages 265-310
Construction of Chaotic Regions....Pages 311-340
Computational Methods....Pages 341-398
Non-Linear Structural Dynamics....Pages 399-435
Back Matter....Pages 436-452

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This work deals effectively and systematically with the main contents of modern analytical methods of nonlinear science, dynamic systems and the basic concepts of the theory and its applications in engineering. While many books consider systems involving only a few unknowns, a real engineering system involves thousands, and this work emphasises the reduction of the number of these unknowns while capturing the essential physical phenomena. Methods of Liapunov-Schmidt reduction, central manifold, normal form and averaging are discussed in detail. Computational methods for harmonic balance, normal form, symplectic integration and invariant torus are studied. Finally, applications to solid mechanics, rotating shaft, flutter and galloping are given. This book can be used as a textbook or reference guide to the subject by undergraduate and postgraduate students studying in areas such as mechanics, mathematics, physics and a wide range of related scientific disciplines. It will also be valuable as a reference book for teachers, researchers and engineering designers.
Content:
Front Matter....Pages i-xii
Dynamical Systems, Ordinary Differential Equations and Stability of Motion....Pages 1-34
Calculation of Flows....Pages 35-65
Discrete Dynamical Systems....Pages 66-83
Liapunov—Schmidt Reduction....Pages 84-153
Centre Manifold Theorem and Normal Form Of Vector Fields....Pages 154-175
Hopf Bifurcation....Pages 176-229
Application of the Averaging Method in Bifurcation Theory....Pages 230-264
Brief Introduction to Chaos....Pages 265-310
Construction of Chaotic Regions....Pages 311-340
Computational Methods....Pages 341-398
Non-Linear Structural Dynamics....Pages 399-435
Back Matter....Pages 436-452
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