412 An Analytical Study of the Changes in Modal Shape of Disk Effects on its Strain Energy

Abstract

In this report, we considered that the effects of in-plane stress of disk for the changes of modal shape analytically. The purpose of this report is to confirm whether the modal shapes change according to the change of in-plane stress. The results clarify the in-plane stress changes the modal shape. The curvature of the modal shape is proportional to reciprocal number of the bending stiffness. The in-plane stress has the effect to change the bending stiffness distributions on disk. Moreover, the natural frequencies of disk are evaluated by two energy methods in which the variations of modal shapes are considered or not. The difference of natural frequencies from two methods shows the effect of the changes of modal shape of disk for difference of results of the energy method is small (the maximum difference of strain energy is 7.1 %).