THE EFFECTS OF SHEAR FLEXIBILITY AND ROTATORY INERTIA ON THE BENDING VIBRATIONS OF BEAMS

Abstract

The paper gives a fairly complete theoretical treatment of the problem of the lateral vibrations of a uniform beam when shear flexibility (but not shear-lag effects) and rotatory inertia are taken into account; frequency equations and model forms are given for the nine cases defined by the various combinations of the three usual types of end support. Considerable attention is directed towards the higher frequencies; one matter of unusual interest is the existence of a second spectrum of frequencies, which has not previously been noted. Formulae are given by means of which it is possible to estimate the effects of shear flexibility and rotatory inertia as corrections to results obtained from studies in which these quantities are ignored. Two numerical examples illustrate the appearence of the second spectrum. A second PARTof the paper describes an experimental investigation conducted on a family of box beams; excellent agreement is obtained with frequencies calculated by the methods of the first part. This investigation shows the considerable importance of shear flexibility and the relative unimportance of rotatory inertia for a box beam of modern design. The paper concludes with a short theoretical study, by means of the ‘segmented’ approach, into the effects of flexibility in shear on the bending vibrations of the wing of the Bristol Brabazon I aeroplane: here also the effect is important.