Analysis of Axial Vibration of Rotating Thick Disk, Based on Transfer Matrix Method : Effects of Shear Deformation, Rotatory Inertia and Centrifugal Tension

Abstract

The analysis of axial vibration of rotating thick disk, the theme of this paper, is an important issue when one analyzes blade-disk-rotor coupled vibration by the substructure synthesis method. This paper presents (1) a proper method of treating shear deformation, rotatory inertia and centrifugal tension, and (2) how the individual effects of each of these three factors depend on disk geometry. The disk is treated as a distributed stiffness and distributed inertia system. Shear deformation is introduced according to Reissner's theory. Rotatory inertia is treated as a result of body inertia force. The centrifugal tension component perpendicular to the elastic curve is a resistance to deflection. Numerical calculations based on the transfer matrix show that (1) the larger the ratio of disk thickness to its outer-minus-inner radius becomes, the larger the effect of shear deformation and rotatory inertia, and the smaller the effect of centrifugal tension become, and (2) the smaller the ratio becomes the smaller the effect of shear deformation and rotatory inertia, and the larger the effect of centrifugal tension become.