Transient Response of Uniform Beams

Citation

Anderson, Roger Alan (1953) Transient Response of Uniform Beams. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/ZVM1-7T63. https://resolver.caltech.edu/CaltechETD:etd-04212003-111122

Abstract

Several special topics relating to the transient flexural vibrations of a uniform beam predicted by the usual elementary or Bernoulli-Euler equation are discussed. The effect on the beam response of the concentration of an applied transient force in space and in time is studied. In the case of an applied step force, it is shown that the dynamic team response can be larger than twice the response to an equal force statically applied. It is demonstrated that the beam response in the higher modes is independent of the boundary conditions. A new, general series solution of the mode superposition type is given for the flexural vibrations of a uniform beam according to the more refined Timoshenko equations including the secondary effects of shear deflections and rotatory inertia. As a special case, the solution is presented for a pin-ended beam. These solutions are characterized by two series, each of the form of the series solution of the Bernoulli-Euler equation. For the special case of a concentrated transient force applied at the midpoint of a pin-ended beam, the bending moment and shear force solutions for the Timoshenko and Bernoulli-Euler equations are compared.

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