Nonlinear Free Vibration of Beams with Clamped Ends and with One End Clamped, Other End Simply Supported

Abstract

In this paper, an approximate solution is given by the use of Galerkin's procedure for the large amplitude free vibration of a beam with immovable clamped ends, subjected to an initial axial load. The results of the vibrations of a beam with one end clamped and other end simply supported are known from those of the vibrations of the antisymmetric modes of a clamped beam. Numerical calculations are carried out for cases of the fundamental vibration of both beams. Finally, a comparison of the increasing rate of the fundamental frequency with the amplitude is made among the beams having different end conditions : both ends clamped, one end clamped and other end simply supported, and both ends simply supported.