Vibration of Strongly Nonlinear Discontinuous Systems

Language: English

Published by Springer, 2010

3642074715 / 9783642074714

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Druck auf Anfrage Neuware - Printed after ordering - 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.

Seller Inventory # 9783642074714

Title
Vibration of Strongly Nonlinear Discontinuous Systems
Author
V. I. Babitsky
Publisher
Springer
Publication year
2010
Condition
Neu
Binding
Taschenbuch
Language
English
ISBN 10
3642074715
ISBN 13
9783642074714
Item weight
639 grams
Dimensions
235x155x23 mm

AHA-BUCH GmbH

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