Non-conservative systems with symmetrizable stiffness matrices exhibiting limit cycles
type: Item
instance of: scholarly article
title: Non-conservative systems with symmetrizable stiffness matrices exhibiting limit cycles
zbMATH Open document ID: 0893.73031
DOI: 10.1016/S0020-7462(96)00070-4
author: A. N. Kounadis
author: George J. Simitses
published in: International Journal of Non-Linear Mechanics
publication date: 1998-08-24T00:00:00Z
review text: The authors examine bifurcational systems having trivial fundamental paths under partial follower loading with non-conservativeness parameter \(n\). The dynamic response of such non-potential systems associated with symmetrizable asymmetric stiffness matrices has been extensively studied earlier by using a linear analysis. The last linear analyses of the above autonomous asymmetric systems gave a behavior similar to that of an associated symmetric (conservative or potential) system exhibiting, when damping is included, either a point attractor or a divergent motion (dynamic buckling). This paper addresses the response of the aforementioned non-potential autonomous dissipative systems using both linear and nonlinear analyses. Attention is focused on whether it is possible for the systems to experience a limit cycle response in regions of existence of adjacent equilibria (region of divergence instability), exhibiting, namely, a behaviour which cannot occur in symmetric (conservative) systems. The analysis deals with systems that are discrete or are discretized by some approximation technique.
Mathematics Subject Classification ID: 74H45
Mathematics Subject Classification ID: 37G99
Mathematics Subject Classification ID: 34C05
zbMATH DE Number: 1079947
zbMATH Keywords: dynamic buckling
zbMATH Keywords: trivial fundamental paths
zbMATH Keywords: point attractor
zbMATH Keywords: non-potential autonomous dissipative systems
reviewed by: J. Genin
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1079947