Vibration of Strongly Nonlinear Discontinuous Systems

2001
ISBN: 978-3-540-41447-6
Verlag: Springer Berlin Heidelberg

Buch, Englisch, 402 Seiten, HC runder Rücken kaschiert, Format (B × H): 160 mm x 241 mm, Gewicht: 1700 g

Reihe: Foundations of Engineering Mechanics

Among the wide diversity of nonlinear mechanical systems, it is possible to distinguish a representative class of the systems which may be characterised by the presence of threshold nonlinear positional forces. Under particular configurations, such systems demonstrate a sudden change in the behaviour of elastic and dissipative forces. Mathematical study of such systems involves an analysis of equations of motion containing large-factored nonlinear terms which are associated with the above threshold nonlinearity. Due to this, we distinguish such discontinuous systems from the much wider class of essentially nonlinear systems, and define them as strongly nonlinear systems'. The vibration occurring in strongly nonlinear systems may be characterised by a sudden and abrupt change of the velocity at particular time instants. Such a vibration is said to be non-smooth. The systems most studied from this class are those with relaxation (Van Der Pol, Andronov, Vitt, Khaikhin, Teodorchik, etc. [5,65,70,71,98,171,181]), where the non-smooth vibration usually appears due to the presence of large nonconservative nonlinear forces. Equations of motion describing the vibration with relaxation may be written in such a manner that the highest derivative is accompanied by a small parameter. The methods of integration of these equations have been developed by Vasilieva and Butuzov [182], Volosov and Morgunov [190], Dorodnitsin [38], Zheleztsov [201], Mischenko and Rozov [115], Pontriagin [137], Tichonov [174,175], etc. In a system with threshold nonlinearity, the non-smooth vibration occurs due to the action of large conservative forces. This is distinct from a system with relaxation.

Zielgruppe

Research

Autoren/Hrsg.

Babitsky, V. I.

Krupenin, V. L.

Weitere Mitwirkende

Veprik, A.

Fachgebiete

• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Maschinenbau
• Naturwissenschaften Physik Mechanik Klassische Mechanik, Newtonsche Mechanik
• Mathematik | Informatik Mathematik Mathematik Interdisziplinär Computeralgebra
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Statik, Dynamik, Kinetik, Kinematik

Inhaltsverzeichnis

1 Operators of Linear Systems.- §1. Dynamic Compliance.- §2. Periodic Green Functions.- §3 Parametric Periodic Green Functions.- 2 Strongly Nonlinear Single-Degree-of Freedom Systems.- §4 Conservative Systems.- §5 Forced Vibration.- §6 Vibration in Autonomous Systems.- §7 Parametric Vibration.- §8 Random Vibration.- 3 Multiple-Degree-of-Freedom Systems.- §9 Forced Vibration in Multiple-Degree-of-Freedom Systems.- §10 Parametric Vibration in the Multiple-Degree-of-Freedom Systems.- Additional Bibliography.- Appendix I The Averaging Method in Systems with Impacts.- Appendix II On the Analysis of Resonant Vibration of Vibro-impact Systems Using the Averaging Technique.- Appendix III Structure-borne Vibroimpact Resonances and Periodic Green Functions.- Appendix IV Nonlinear Correction of a Vibration Protection System Containing Tuned Dynamic Absorber.