Vibration of functionally graded disks

In this study, the undamped and damped transverse vibration of a rotating functionally graded (FG) disk with variable geometry is analyzed using a finite element program. The material properties and geometry of the disk are assumed the change in the radial direction according with the powerlaw function. The vibration responses of the annular disks are obtained for the Free-Free (F-F), Clamped-Free (C-F) and Clamped-Clamped (C-C) boundary conditions at the inner and outer surfaces, and Campbell diagrams are drawn to see the effects of the rotational velocities on frequencies. The change of frequencies of FG disks depending on the rotational velocity is obtained for the forward and backward waves of some modes. The fact that the frequencies obtained from the present study and the literature are very close to each other, proves the accuracy of the study. Although in a non-rotating disk there is only one natural frequency for each (m, n) mode, in rotating disks all modes with a nodal diameter have two different natural frequencies. For each mode, the difference between increasing and decreasing frequency values according to the whirl direction openmore as the rotational velocity increases. With the increase in the material index, there is a decrease in the frequency values in all modes. As the geometric index decreases, there are huge increases in frequencies. The frequencies increases lightly for C-F disks, and even increase significantly for C-C disks, as compared to the frequencies of F-F disks. The results of the present study are compatible with the results in literatures.