Abstract
Based on the finite element method, a new analytical procedure on free flexural vibrations of a stepped beam is presented. In this analysis, the stepped beam is divided roughly into the segments with different cross section. The mode shape function proposed by senior author is introduced to discretized equation derived by the Galerkin procedure. This function expressed by the product of the truncated power series and the trigonometric function is continuously differentiable. The continuity conditions of deflection, slope, bending moment, and shear force are satisfied in the nodes of each segment. We call the name of this procedure as the Finite Segment Analysis. The natural frequencies of a straight beam are analyzed, and the accuracy of the numerical procedure is discussed. Changing dimensions of the stepped beam, the natural frequencies and the natural modes of vibration are compared. Accurate results of natural frequencies and the natural modes of vibration are obtained with a small number of segments.
