Frequency analysis of axially loaded stepped beams by Greenʹs function method

This paper presents a solution to a free vibration problem of stepped beams loaded by axial forces. The frequency equation is obtained by using properties of the Greenʹs functions corresponding to uniform segments of the beam. The approach pertains to the vibration of beams consisting of an arbitrary number of uniform segments. The method can be used to obtain an approximate solution to vibration problems of beams with continuously varying cross-sections. Numerical examples are presented to demonstrate the usefulness of the method in the frequency analysis of stepped beams.