A slender, straight beam resting on a flat, rigid foundation does not buckle when subjected to a compressive load, since the load cannot overcome the effect of the beam’s weight. However, it buckles if its ends are moved toward each other. Post-buckling of such a beam is examined, both theoretically and experimentally, for horizontal and inclined foundations. The beam is modeled as an elastica, and equilibrium states with large deflections are computed, including cases in which self-contact occurs. Frequencies and mode shapes for small vibrations about equilibrium are also determined. Agreement between the theoretical and experimental results is very good.
Post-bauckling and Vibration of Heavy Beam on Horizontal or Inclined Rigid Foundation
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Santillan, S. T., Virgin, L. N., and Plaut, R. H. (October 27, 2005). "Post-bauckling and Vibration of Heavy Beam on Horizontal or Inclined Rigid Foundation." ASME. J. Appl. Mech. July 2006; 73(4): 664–671. https://doi.org/10.1115/1.2165237
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