Free Vibration Analysis for Cracked FGM Beams by Means of a Continuous Beam Model

Figure 6

The first three frequency ratios of hinged-hinged isotropic homogenous beams with different slenderness ratios and containing a single open edge crack of varying depths: (a) the fundamental frequency ratio, (b) the second frequency ratio, and (c) the third frequency ratio.

(a)  

(b)

(c)