ON THE DYNAMIC BUCKLING MECHANISM OF SINGLE-DEGREE-OF-FREEDOM DISSIPATIVE/NON-DISSIPATIVE AUTONOMOUS SYSTEMS

The dynamic global response of single-degree-of-freedom dissipative/non-dissipative gradient discrete systems described by non-linear autonomous ordinary differential equations is thoroughly studied by using energy criteria. Emphasis is given to the study of the dynamic buckling mechanism (always occurring via a saddle) and the associated long term response of the escaped motion. To this end, the dynamic responses of two non-linear models (with a variety of equilibrium configurations) subjected to a suddenly applied load of infinite duration are examined in detail. It is found that dynamic buckling may lead sometimes to an unbounded motion regardless of the existence of another remote stable equilibrium position, while in other cases the latter position may act as point attractor capturing the motion. Moreover, it is established that the stable equilibrium positions of a complementary equilibrium path do not act as point attractors, as may occur in case of multi-degree-of-freedom systems. Finally, exact (for non-dissipative) and very good lower and upper bounds (for dissipative) systems are presented.