Short Remark on Lateral Vibration of Functionally Graded Beams

Abstract

In his study Aydogdu analyzes the vibration of axially functionally graded simply supported beams. The main idea behind his calculation is that the vertical displacement is supposed to have a special form, which transforms the Euler-Bernoulli differential equation for the motion for the lateral vibrations into an exact linear differential equation which depends on the axial coordinate only. In this paper we generalize the method used by Aydogdu and determine the largest function class of the form w(x,t) = F(x) • G(t) for which the same method is applicable.