Damping in Initially Stressed Elastically Unstable Structures

Abstract

1 The vibration response (natural frequencies and damping) of a 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 (simply-supported) beam is treated approximately as two-bar link with a rotational spring and damper at the mid-span. 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, while the modal damping increases from underdamped to overdamped. As this load approaches the buckling load, the beam natural frequency goes to zero, while the modal damping approaches infinity. Once the beam deforms into its post-bucked state, then further increases in the compression loading causes an increase in the beam bending natural frequency and the corresponding modal damping goes from infinity to overdamped to finally underdamped. The natural frequency and damping of the post-buckled beam approach that of the initially unloaded beam as the beam deformation is fully collapsed. 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.