Transverse Vibrations of Tapered Cantilever Beams with End Loads

Abstract

Free vibrations of nonuniform cantilever beams with an end mass have been investigated, using the equations of Bernoulli-Euler. Two configurations of interest are treated: (a) constant width and linearly variable thickness; and (b) constant thickness and linearly variable width. Charts have been plotted for each case from which the fundamental frequency, the second harmonic, and the third harmonic can be easily determined for various taper ratios and ratios of end mass to beam mass. The Tables from which these charts were plotted are also included.