QUALITATIVE CRITERIA IN NONLINEAR DYNAMIC BUCKLING AND STABILITY OF AUTONOMOUS DISSIPATIVE SYSTEMS

A general qualitative approach for dynamic buckling and stability of a utonomous dissipative structural systems is comprehensively presented. Attention is focused on systems which under the same statically appli ed loading exhibit a limit point instability or an unstable branching point instability with a non-linear fundamental path. Using the total energy equation, the theory of point and periodic attractors of the ba sin of attraction of a stable equilibrium point, of local and global b ifurcations, of the inset and outset manifolds of a saddle and of the geometry of the channel of motion, the stability of the fundamental eq uilibrium path and the mechanism of dynamic buckling are thoroughly di scussed. This allows us to establish useful qualitative criteria leadi ng to exact, approximate and upper/lower bound buckling estimates with out integrating the highly non-linear initial-value problem. The indiv idual and coupling effect of geometric and material non-linearities of damping and mass distribution on the dynamic buckling load are also e xamined. A comparison of the results of the above qualitative analysis with those obtained via numerical simulation is performed on several two- and three-degree-of-freedom models of engineering importance. Cop yright (C) 1996 Published by Elsevier Science Ltd.