NDLI: A paradigmatic minimal system to explain the Ziegler paradox

Content Provider	Springer Nature Link
Author	Luongo, Angelo D’Annibale, Francesco
Copyright Year	2014
Abstract	The destabilization effect of damping on a class of general dynamical systems is discussed. The phenomenon of jump in the critical value of the bifurcation parameter, in passing from undamped to damped system, is view in a new perspective, according to which no discontinuities manifest themselves. By using asymptotic analysis, it is proved that all subcritically loaded undamped systems are candidate to become unstable, provided a suitable damping matrix is added. The mechanism of instability is explained by introducing the concept of modal dampings, as the components of the damping forces along the unit vectors of a non-orthogonal eigenvector basis. Such quantities can change sign while the load changes the eigenvectors of the basis, thus triggering instability. A paradigmatic, non-physical, minimal system has been built up, admitting closed-form solutions able to explain the essence of the destabilizing phenomenon. Series expansions carried out on the exact solution give information on how to deal more complex systems by perturbation methods.
Starting Page	211
Ending Page	222
Page Count	12
File Format	PDF
ISSN	09351175
Journal	Continuum Mechanics and Thermodynamics
Volume Number	27
Issue Number	1-2
e-ISSN	14320959
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2014-05-25
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Ziegler paradox Damping destabilization Circulatory Hopf bifurcation Generic Hopf bifurcation Perturbation methods Classical Continuum Physics Engineering Thermodynamics, Heat and Mass Transfer Theoretical and Applied Mechanics Structural Materials
Content Type	Text
Resource Type	Article
Subject	Physics and Astronomy Mechanics of Materials Materials Science

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