FREE VIBRATION ANALYSIS OF EDGE CRACKED FUNCTIONALLY GRADED BEAMS RESTING ON WINKLER-PASTERNAK FOUNDATION

Abstract

In this study, free vibration analysis of an edge cracked functionally graded cantilever beam resting on WinklerPasternak foundation. Material properties of the beam change in the thickness direction according to exponential distributions. The differential equations of motion are obtained by using Hamilton’s principle. The considered problem is investigated within the Euler-Bernoulli beam theory by using finite element method. The cracked beam is modeled as an assembly of two sub-beams connected through a massless elastic rotational spring. In the study, the effects of the location of crack, the depth of the crack, foundation stiffness and various material distributions on the natural frequencies and the mode shapes of the cracked functionally graded beams are investigated in detail