Non-conservative systems with symmetrizable stiffness matrices exhibiting limit cycles
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.
non-potential autonomous dissipative systems
scientific article; zbMATH DE number 1079947