Accession Number : AD0006031


Title :   A METHOD FOR CALCULATING THE NATURAL FREQUENCIES OF CONTINUOUS BEAMS


Corporate Author : ILLINOIS UNIV AT URBANA ENGINEERING EXPERIMENT STATION


Personal Author(s) : Veletsos, A S ; Newmark, N M


Full Text : https://apps.dtic.mil/dtic/tr/fulltext/u2/006031.pdf


Report Date : Jan 1953


Pagination or Media Count : 44


Abstract : A method is described for calculating the undamped natural frequencies of the flexural vibration of elastic beams which are continuous over nondeflecting supports. The method is analogous to Holzer's method (Holzer, H., Die Berechunug der Drechschwingungen, J. Springer, Berlin, 1921) and reduces to a routine tabular scheme of computation. A sufficient number of repetitions provides the natural frequencies to any desired degree of accuracy. The beams were assumed to be straight but were allowed any number of spans of arbitrary length. The ends were permitted to be hinged, fixed, or only partially fixed through rotational restraints. These were assumed to be proportional to the end rotations. A variation in the cross section and the mass/unit length from one span to the other was permitted; however, these were assumed to be constant for given span. The vibration was restricted to a principal plane of beam flexure, and the effects of shearing deformation rotational inertia were disregarded. The method was illustrated by a numerical example. Numerical values are appended for (1) dynamic flexural stiffness, and (2) the product of dynamic flexural stiffness and dynamic flexural carry-over factor.


Descriptors :   *BEAMS(STRUCTURAL) , *RESONANT FREQUENCY , DYNAMICS , MASS , DEFORMATION , FLEXURAL PROPERTIES , LENGTH , CROSS SECTIONS , TABLES(DATA) , RESTRAINT , ROTATION , INERTIA , VIBRATION , STIFFNESS


Subject Categories : Mechanics


Distribution Statement : APPROVED FOR PUBLIC RELEASE