Buch, Englisch, 397 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 756 g
Buch, Englisch, 397 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 756 g
Reihe: Foundations of Engineering Mechanics
ISBN: 978-3-540-41001-0
Verlag: Springer
This text maps out the modern theory of non-linear oscillations. The material is presented in a non-traditional manner and emphasises the new results of the theory - obtained partially by the author, who is one of the leading experts in the area. Among the topics are: synchronization and chaotization of self-oscillatory systems and the influence of weak random vibration on modification of characteristics and behaviour of the non-linear systems.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Technische Wissenschaften Maschinenbau | Werkstoffkunde Maschinenbau
- Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Statik, Dynamik, Kinetik, Kinematik
- Naturwissenschaften Physik Mechanik
- Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
- Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
Weitere Infos & Material
1. Introduction.- 1.1 The importance of oscillation theory for engineering mechanics.- 1.2 Classification of dynamical systems. Systems with conservation of phase volume and dissipative systems.- 1.3 Different types of mathematical models and their functions in studies of concrete systems.- 1.4 Phase space of autonomous dynamical systems and the number of degrees of freedom.- 1.5 The subject matter of the book.- 2. The main analytical methods of studies of nonlinear oscillations in near-conservative systems.- 2.1 The van der Pol method.- 2.2 The asymptotic Krylov-Bogolyubov method.- 2.3 The averaging method.- 2.4 The averaging method in systems incorporating fast and slow variables.- 2.5 The Whitham method.- I. Oscillations in Autonomous Dynamical Systems.- 3. General properties of autonomous dynamical systems.- 4. Examples of natural oscillations in systems with one degree of freedom.- 5. Natural oscillations in systems with many degrees of freedom. Normal oscillations.- 6. Self-oscillatory systems with one degree of freedom.- 7. Self-oscillatory systems with one and a half degrees of freedom.- 8. Examples of self-oscillatory systems with two or more degrees of freedom.- 9. Synchronization and chaotization of self-oscillatory systems by an external harmonic force.- 10. Interaction of two self-oscillatory systems. Synchronization and chaotization of self-oscillations.- 11. Interaction of three or more self-oscillatory systems.- II. Oscillations in Nonautonomous Systems.- 12. Oscillations of nonlinear systems excited by external periodic forces.- 13. Parametric excitation of oscillations.- 14. Changes in the dynamical behavior of nonlinear systems induced by high-frequency vibration or by noise.- A. Derivation of the approximate equation for the one-dimensional probability density.- References.
