A METHOD FOR CALCULATING THE NATURAL FREQUENCIES OF CONTINUOUS BEAMS

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 Holzers 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 massunit 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.