Transverse vibration and stability of a functionally graded rotating annular disk with a circumferential crack

The in-plane disk stresses are obtained using a semi-analytical approach. Those in plane stresses are used to obtain the governing equation of out of plane motion of the disk. A finite difference scheme is used to solve the partial differential equation of motion to obtain eigenvalues, critical speed and associated mode shapes. The lowest critical speed, which is one of the important parameters limiting the performance of the rotating disk, is obtained from the Campbell Diagram. It is found that irrespective of the distribution of the modulus of elasticity in the FG disk, increasing the crack depth or decreasing the crack radial distance from the disk center decreases the critical speed. The critical speed reduction is more pronounced for the case when the disk material modulus of elasticity is decreasing from the disk center.