Effects of Shear Deformation and Rotary Inertia on the Free Vibration of a Rotating Annular Plate

Abstract

This Tech Brief addresses the effects of shear deformation and rotary inertia on the free vibration of a rotating annular plate. Several studies have been done to understand these effects (Irie et al, 1982; Sinha, 1987). In particular, the importance of these terms is well known for disks with a thickness ratio h/a > 0.05 where h is the thickness of the disk and a is its outer radius. However, there is a need to show how they affect the disk vibration as the thickness ratio increases. It is well accepted that shear deformation and rotary inertia should be included in the analysis when h/a > 0.05 (Batoz and Dhatt, 1990). However, this Tech Brief will show that this criterion is not valid for all the modes. It will present the evolution of the number of modes correctly evaluated versus the thickness ratio, and, finally, will give a heuristic criterion to predict when it is necessary to consider shear deformation and rotary inertia.