Accession Number : AD0013062


Title :   FORCED MOTIONS OF TIMOSHENKO BEAMS


Corporate Author : COLUMBIA UNIV NEW YORK


Personal Author(s) : Herrmann, G


Full Text : https://apps.dtic.mil/dtic/tr/fulltext/u2/013062.pdf


Report Date : Jun 1953


Pagination or Media Count : 25


Abstract : In attempting a complete solution for the general forced vibration problem, the homogeneous differential equations of motion (with homogeneous boundary conditions) were set up for the free vibrations of beams. These equations were satisfied for an infinite set of discrete frequencies each of which corresponds to a mode shape. Rayleigh's method (Theory of Sound, p. 262, Dover Publications, N. Y., 2nd ed., 1945) was then used to formulate the orthogonality property for the principal modes of free vibration. By using these results and the procedures of Mindlin and Goodman (Am. Soc. Mech. Eng. Paper 49-A-19, 1949) for time-dependent boundary conditions, the general problem of forced motion was reduced to a free vibration problem and a quadrature.


Descriptors :   *TIMOSHENKO BEAM , VIBRATION , TIME DEPENDENCE , SHAPE , MOTION , DIFFERENTIAL EQUATIONS , INFINITE SERIES , SET THEORY , ORTHOGONALITY , HOMOGENEITY , FREQUENCY , SOUND


Subject Categories : Mechanics


Distribution Statement : APPROVED FOR PUBLIC RELEASE