The Concept of Dynamic Stability

Abstract

The beginning of dynamic instability and/or dynamic buckling can be traced to the investigation of Koning and Taub [1], who analyzed a suddenly loaded (in the axial direction) imperfect, simply supported column. Several studies followed in the 1940s and 1950s on the problem of dynamic column buckling. These studies [2–7] concentrated on such effects as those of axial inertia, of short and long duration of the load, of low- and high-velocity excitation, of in-plane inertia, of rotatory inertia, and of transverse shear. Similar studies continued into the 1970s [8–18] and the 1980s [19–20]. Moreover, nondeterministic consideration was included by Elishakoff [21–22] and extensions to plate geometries were reported by others [23–27]. A detailed discussion of geometries of this type is presented in Chapter 10. For these geometries, which under static conditions experience smooth buckling (the analysis shows that there exists s bifurcation point and the postbucking branch corresponds to stable static equilibrium positions), there is no clear criterion of instability, although the criterion used for establishing critical conditions is very simple. When some characteristics deflection increases rapidly with time, we have a dynamically critical condition. In reality, the problem of suddenlyy loaded columns and plates is one of dynamic response rather than one that encounters escaping (bucked) motion of some types. Parametric resonance is a possible dynamic instability for these configurations (see[28]).