Damping Variations in Post-Buckled Structures Having Geometric Imperfections

Abstract

The vibration response (natural frequencies and damping) of a geometrically-imperfect post-buckled beam as a result of an axial compression force is studied both analytically as well as experimentally. In the analytical development, the pinned-pinned (simplysupported) beam with geometric imperfections is treated approximately as two-bar link with a rotational spring and damper at the mid-span. Here the geometric imperfection is treated as an applied load acting with an offset to the beam centroid so that the load application will produce an applied compression load as well as a bending moment. For the case of no imperfections, it is shown that the post-buckled beam vibrational behavior follows inversely to the behavior of the pre-buckled beam vibrational behavior. For example, as one applies an increasing compression load to a prebuckled beam, the natural frequencies decrease to zero as the beam buckles and then increase significantly as the beam is in its post-buckled state. Likewise the experimentally measured modal damping increases to infinity as the beam buckles and then returns to its initial value in its post-buckled state. But when geometric imperfections are present, the beam does not experience a unique bifurcation state, instead starts slowly buckling at the onset of the applied load. In this case, the natural frequencies are shown to decrease initially and then increase for large deformations. Likewise, the experimentally measured modal damping increase initially and then decrease. Experimental testing of a compressively loaded graphite/epoxy beam validate these trends for both the pre-buckled and post-buckled conditions. These results are of interest to designers of compressively loaded structures that are subject to buckling, for example fuselage and wing skins that are subjected to dynamic loads.