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Dissipation induced instabilities in continuous non‐conservative systems
Author(s) -
Kirillov Oleg N.,
Seyranian Alexander P.
Publication year - 2005
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200510029
Subject(s) - dissipation , eigenvalues and eigenvectors , viscoelasticity , stability (learning theory) , domain (mathematical analysis) , boundary (topology) , control theory (sociology) , mechanics , mathematics , physics , classical mechanics , mathematical analysis , computer science , thermodynamics , control (management) , quantum mechanics , machine learning , artificial intelligence
In this contribution we analyze the stabilizing and destabilizing effect of small damping for rather general class of continuous non‐conservative systems, described by the non‐self‐adjoint boundary eigenvalue problems. Explicit asymptotic expressions obtained for the stability domain allow us to predict when a given combination of the damping parameters leads to increase or to decrease in the critical non‐conservative load. The results obtained explain why different types of internal and external damping so surprisingly influence on the stability of non‐conservative systems. As a mechanical example the stability of a viscoelastic rod with small internal and external damping, loaded by tangential follower force, is studied in detail. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)