Accession Number : AD0013061


Title :   TIMOSHENKO'S SHEAR COEFFICIENT FOR FLEXURAL VIBRATIONS OF BEAMS


Corporate Author : COLUMBIA UNIV NEW YORK


Personal Author(s) : MINDLIN, R D ; DERESIEWICZ, H


Full Text : https://apps.dtic.mil/dtic/tr/fulltext/u2/013061.pdf


Report Date : Jun 1953


Pagination or Media Count : 25


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.


Descriptors :   *COEFFICIENTS , CROSS SECTIONS , DEFLECTION , ELASTIC PROPERTIES , EQUATIONS , FREQUENCY , RECTANGULAR BODIES , SHEAR PROPERTIES , TRANSVERSE , VIBRATION


Subject Categories : Numerical Mathematics


Distribution Statement : APPROVED FOR PUBLIC RELEASE