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Nonlinear Stability and Dynamic Buckling of Autonomous Dissipative Systems
Author(s) -
Kounadis A. N.
Publication year - 1995
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19950750414
Subject(s) - dissipative system , buckling , nonlinear system , discontinuity (linguistics) , imperfect , stability (learning theory) , saddle point , structural stability , path (computing) , saddle , control theory (sociology) , mathematics , computer science , classical mechanics , mathematical analysis , physics , structural engineering , geometry , engineering , mathematical optimization , linguistics , philosophy , control (management) , quantum mechanics , machine learning , artificial intelligence , programming language
An analytical approach for the stability and the dynamic buckling response of multiple‐parameter dissipative systems described by autonomous differential equations is presented. Attention is focused on general imperfect structural systems with or without symmetric imperfections including statically stable systems which display also an unstable complementary path. The significance of the unstable (physcial or complementary) path, of the basin of attraction of stable equilibria, and of the inset and outset manifolds of a saddle on the dynamic buckling mechanism is comprehensively examined with the aid of basic theorems of local dynamic analysis. A contradiction between local and global dynamic analysis as well as cases of dynamic buckling with sensitivity to initial conditions and damping, discontinuity and metastability phenomena are also explored. Three simple dissipative systems of structural engineering importance are used as illustrative models.