Effect of the Weight of Beam on the Measurement of Young's Modulus by Lateral Vibration of Cantilevers

TLDR: In this paper, the first and second frequencies of a cantilever were derived from the equation of motion of the beam subjecting along the length of a beam to a uniformly distributed load, and the experimental results for the fundamental vibration of cantilevers were presented.

Abstract: The amount of effect of the weight of beam on the measuring values of Young's modulus by latelal vibration of cantilevers may be given by considering only the component of weight acting in the direction of the length of the beam. In this paper the approximate solutions of the first and second frequencies of cantilever, by using the Galerkin method, are given from the equation of motion of the beam subjecting along the length of the beam to a uniformly distributed load. Accordingly the calculating equations of Young's modulus are obtained from these solutions. And the experimental results for the fundamental vibration of cantilevers is presented. It is shown that the Young's modulus can be measured exactly by treating the experimental results with these corrected equations.