Vibrations of cracked functionally graded beams: General solution and application – A review

This paper presents a unified approach to vibration analysis of functionally graded beams with transverse open-edge cracks based on the so-called vibration shape obtained as a general solution of vibration equations in the frequency domain. The crack is modeled by a pair of translational and rotational springs of stiffness computed from the crack depth in dependence upon functionally graded material parameters. The frequency-dependent vibration shape functions allow one not only to obtain the closed-form solution of both free and forced vibrations for multiple cracked FGM beams but also to develop the well-known methods such as Transfer Matrix Method or Dynamic Stiffness Method for analysis of FGM framed structures. The proposed theoretical developments have been illustrated by their application for modal analysis and frequency response analysis of multi-span and multistep beams.