Free Vibrations of a Circular Rod with an Elastically Restrained End and a Free End

摘要

An analytical evaluation of an experimental procedure involving the free flexural vibrations of a clamped beam of circular cross section has been carried out. This work was undertaken in order to explain why certain experimental results seem to indicate that Young's modulus E decreases as the length to diameter ratio of the beam decreases. Under the assumption that E remains constant, the analysis indicates that the boundary condition of vanishing slope at the clamped end is not realized in the laboratory. Using a modified boundary condition and a perturbation technique, a corrected relationship for E is obtained. (Author)