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Transient Response of Uniform Beams


Anderson, Roger Alan (1953) Transient Response of Uniform Beams. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/ZVM1-7T63.


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.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:(Mechanical Engineering and Physics)
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Mechanical Engineering
Minor Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Hudson, Donald E.
Thesis Committee:
  • Unknown, Unknown
Defense Date:1 January 1953
Record Number:CaltechETD:etd-04212003-111122
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1432
Deposited By: Imported from ETD-db
Deposited On:21 Apr 2003
Last Modified:17 May 2023 22:20

Thesis Files

PDF (Anderson_ra_1953.pdf) - Final Version
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