TIMOSHENKO'S SHEAR COEFFICIENT FOR FLEXURAL VIBRATIONS OF BEAMS

Abstract

Timoshenko's shear coefficient for flexural vibrations of beams was computed for circular, elliptical, parabolic, and oval cross sections. A formula for the shear coefficient was obtained by calculating the frequency (from the free-vibration equations of Timoshenko) at which an infinite beam vibrates without transverse deflections and by equating this with the frequency calculated from the 3-dimensional equations of small vibrations of an elastic body. Approximate frequencies obtained by Hidaka (Mem. Imp. Marine Observ., Kobe, Japan 4:99-219, 1931) were used for the ovals, but the other frequencies, as calculated from the equations for small vibrations, were exact. The calculated shear coefficients were tabulated, and all were within about 10% of the coefficient for the rectangular section.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1953
Accession Number
AD0013061

Entities

People

  • H. Deresiewicz
  • R.d. Mindlin

Organizations

  • Columbia University

Tags

Communities of Interest

  • Weapons Technologies

DTIC Thesaurus Topics

  • Aeronautical Engineering
  • Air Force
  • Civil Engineering
  • Engineering
  • Equations
  • Frequency
  • Materials
  • Mechanical Engineering
  • Mechanics
  • Military Research
  • Navy
  • New York
  • Physics
  • Physics Laboratories
  • Rhode Island
  • Shear Stresses
  • Three Dimensional

Fields of Study

  • Engineering

Readers

  • Structural Dynamics.