The Effect of Shear Flexibility and Rotatory Inertia on the Natural Frequencies of Uniform Beams

Abstract

SummaryAn energy approach has been used to obtain approximations to the natural frequencies of uniform beams when the effects of shear flexibility and rotatory inertia are included. The characteristic functions of simple beams are used to describe the bending deflection and the necessity for an assumed shear deflection shape has been eliminated by the use of simple relationships which exist between the effects of shear flexibility and rotatory inertia. A comparison of the approximate frequencies with the exact frequencies shows good agreement even at the higher frequencies. The method has been applied to hinged-hinged, fixed-free, free-free, fixed-fixed, fixed-hinged and free-hinged beams.