Some new instability aspects for nonconservative systems under follower loads

Abstract The mechanism of instability of nonlinear nonconservative discrete systems under follower loads with or without pre-critical deformation is thoroughly re-examined with the aid of a complete nonlinear dynamic analysis. Considering the stability of motion in the large, in the sense of Lagrange, the critical (divergence or dynamic) load is defined as the minimum load for which an unbounded (divergent) motion is initiated. Regions which have been considered (on the basis of linearized analyses) as of flutter instability are found (using a nonlinear dynamic analysis) dynamically stable. Some new instability phenomena contradict existing findings which have been widely accepted. Moreover, it is established that the divergence buckling loads, obtained by static methods of analysis, coincide with the nonlinear dynamic loads only in the case of no pre-critical deformation. Cases of random-like (or chaotic-like) motions for certain values of the nonconservativeness loading parameter are also revealed for autonomous non-dissipative structural systems.

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