Mode Shape Analysis of Multiple Cracked Functionally Graded Timoshenko Beams

The present paper addresses free vibration of multiple cracked Ti-moshenko beams made of Functionally Graded Material (FGM). Cracks are modeled by rotational spring of stiffness calculated from the crack depth and material properties vary according to the power law throughout the beam thickness. Governing equations for free vibration of the beam are formulated with taking into account actual position of the neutral plane. The obtained frequency equation and mode shapes are used for analysis of the beam mode shapes in dependence on the material and crack parameters. Numerical results validate usefulness of the proposed herein theory and show that mode shapes are good indication for detecting multiple cracks in Ti-moshenko FGM beams.