New Instability Aspects for Nonlinear Nonconservative Systems with Precritical Deformation

Summary

The large displacement and time response of a two-degree-of freedom,dissipative, nonlinear cantilever-model under a partial follower load is discussed by using a complete nonlinear dynamic analysis. Considering the stability of motion in the large, in the sense of Lagrange,the mechanism of dynamic instability is thoroughly reexamined for perfect or imperfect systems. New findings for the stability of critical states contradict existing results based on linearized analyses. Critical states of divergence or of nonexistence of adjacent equilibrium may be stable or unstable depending on the amount of material nonlinearity.The nonlinear static buckling loads coincide with the corresponding dynamic ones when there is no precritical deformation; otherwise the latter loads are always less than the former.It was also found that systems statically stable may be proven unstable when a nonlinear dynamic analysis is employed. Clobal bifurcations have revealed that this autonomous system even when damping is excluded may exhibit phenomena looking like chaos.