Modal Analysis of a Multi-cracked FG Shaft Using Finite Element Method

In the current work, a natural frequency analysis of FG shaft having transverse surface cracks using finite element (FE) model is presented. Timoshenko beam element is used for shaft modelling, and the power law material gradation is applied to vary the FG elastic properties in the radial direction. The altered stiffness matrix of the cracked FG shaft in the FE analysis is computed using concepts of fracture mechanics along with Castigliano's theorem to determine LFCs. The behaviour of the multi-cracked FG shaft is analysed using analytic simulation. The amplitude of LFCs is substantially affected by the material gradient index, impacting the performance. Multiple cracks further reduce the stiffness of the shaft. As the gradation index, crack size and crack's distance from end supports are increased, the natural frequency of the shaft is decreased.