In-plane free vibration of circular annular rotating disks

In many engineering applications involving circular disks such as railway wheels, grinding wheels, disk brakes etc. the in-plane dynamics of rotating disks can play a prominent role causing disk noise and vibration. This paper presents a generalized formulation for analysis of in-plane modal characteristics of circular annular rotating disks under different support conditions at the inner and outer boundaries. The in-plane free vibration of the elastic and isotropic disk is studied on the basis of the two-dimensional linear plane stress theory of elasticity. The boundary characteristic orthogonal polynomials are employed in the Lagrange's equation to obtain the natural frequencies and associated mode shapes. Boundary characteristic orthogonal polynomials are generated for the free boundary conditions of the disk while artificial springs are used to account for different boundary conditions. The frequencies corresponding to the forward and backward traveling waves are obtained and compared with those available in the published studies. The proposed formulation is further applied to study the effect of partial constraints on the in-plane vibration characteristics of the rotating disk.