Correlating dynamic bifurcations with impedance measures for multistable structures

Slender, lightweight structures are demanded to meet efficiency targets or to enhance vehicle system performance characteristics. Yet, when subjected to static stress for load-bearing purposes, the flexible structural members may buckle. Furthermore, additional dynamic excitations may activate adverse snap-through responses in such post-buckled components, which accelerates fatigue and failure. The severe nonlinearity associated with these phenomena challenges traditional forms of analysis and necessitates studious experimental methods for conclusive system characterization and model validation. This research builds upon state-of-the-art analytical and experimental strategies to examine the complex forced, dynamic behaviors of built-up structures that contain one or more post-buckled members. An analytical modeling and solution formulation is reviewed that is uniquely amenable to the study of multistable structures and permits experimentally-observable measures of impedance to be identified. Through theoretical and experimental studies, the efficacy of the impedance measures is evaluated towards their usefulness in identifying the onset of dynamic bifurcations in the multistable structural dynamics. For moderate amplitudes of input energy, the analysis is found to provide qualitatively accurate prediction of the drive point impedance changes observed prior to dynamic bifurcations from low to high amplitude of displacement.