Nonlinear Vibrations of a Beam With Pinned Ends

[+] Author and Article Information
J. D. Ray

Research Institute, University of Oklahoma, Norman, Okla.

C. W. Bert

University of Oklahoma, Norman, Okla.

J. Eng. Ind 91(4), 997-1004 (Nov 01, 1969) (8 pages) doi:10.1115/1.3591786 History: Received December 19, 1968


This paper describes theoretical and experimental investigations of the large-amplitude vibrations of a flexible beam simply supported on a nearly rigid base. The beam is designed to minimize most secondary effects, such as transverse shear flexibility, rotatory inertia, and nonlinearities in curvature and in the stress-strain curve. Detailed attention is given to quantitative verification of the assumptions made in deriving the equation of motion. Three different approaches are used to solve the equation: assumed-space mode, assumed-time mode, and Ritz-Galerkin solutions. In the experiments, the beam was base excited. The resonant frequencies and associated strain distributions, modal shapes, and waveforms were measured for various values of initial tension and amplitude ratios (ratio of maximum amplitude to beam thickness) up to 16. Within experimental accuracy, the experimental results verified all of the assumptions made in the analyses. However, no one method of solution resulted in the best predictions of all of the experimentally observed phenomena.

Copyright © 1969 by ASME
Your Session has timed out. Please sign back in to continue.





Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In