An. Kounadis, QUALITATIVE CRITERIA IN NONLINEAR DYNAMIC BUCKLING AND STABILITY OF AUTONOMOUS DISSIPATIVE SYSTEMS, International journal of non-linear mechanics, 31(6), 1996, pp. 887-906
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.