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 shape obtained as general solution equations in frequency domain. The crack is modeled by pair translational and rotational springs stiffness computed from depth dependence upon material parameters. frequency-dependent functions allow one not only obtain closed-form both free forced vibrations for multiple cracked FGM but also develop well-known methods such Transfer Matrix Method or Dynamic Stiffness framed structures. proposed theoretical developments have been illustrated their application modal response multi-span multistep beams.