Theory of Receptance Applied to Modal Analysis of a Spinning Disk With Interior Multi-Point Supports

Abstract

The theory of receptance applied to the modal analysis of a spinning disk with interior multi-point supports is developed. Traveling modes are first introduced for the vibration analysis of a spinning disk. The receptance method is then applied to join the spinning disk and the point supports. The frequency equation and mode shapes are then formulated. An important property, conjugate pairing of the cross receptances is derived. This feature has never been described before in the literature. Numerical results for various numbers of point supports are illustrated. The results show that the nodal pattern of a spinning disk with point supports is varying periodically. The change of rotation speed further causes the mode exchange phenomenon. The change of first critical speed due to point supports is also discussed.