Transient response of uniform beams

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 ap...

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Main Author: Anderson, Roger Alan
Format: Others
Published: 1953
Online Access:https://thesis.library.caltech.edu/1432/1/Anderson_ra_1953.pdf
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 <https://resolver.caltech.edu/CaltechETD:etd-04212003-111122>
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spelling ndltd-CALTECH-oai-thesis.library.caltech.edu-14322019-12-21T03:03:14Z Transient response of uniform beams Anderson, Roger Alan 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. 1953 Thesis NonPeerReviewed application/pdf https://thesis.library.caltech.edu/1432/1/Anderson_ra_1953.pdf https://resolver.caltech.edu/CaltechETD:etd-04212003-111122 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 <https://resolver.caltech.edu/CaltechETD:etd-04212003-111122> https://thesis.library.caltech.edu/1432/
collection NDLTD
format Others
sources NDLTD
description 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.
author Anderson, Roger Alan
spellingShingle Anderson, Roger Alan
Transient response of uniform beams
author_facet Anderson, Roger Alan
author_sort Anderson, Roger Alan
title Transient response of uniform beams
title_short Transient response of uniform beams
title_full Transient response of uniform beams
title_fullStr Transient response of uniform beams
title_full_unstemmed Transient response of uniform beams
title_sort transient response of uniform beams
publishDate 1953
url https://thesis.library.caltech.edu/1432/1/Anderson_ra_1953.pdf
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 <https://resolver.caltech.edu/CaltechETD:etd-04212003-111122>
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