Limitation on Increasing the Critical Speed of a Spinning Disk Using Transverse Rigid Constraints, An Application of Rayleigh's Interlacing Eigenvalues Theorem

Abstract

It can be predicted by Rayleigh's interlacing eigenvalue theorem that structural modifications of a spinning disk can shift the first critical speed of the system up to a known limit. In order to corroborate this theorem, it is shown numerically, and verified experimentally that laterally constraining of a free spinning flexible thin disk with tilting and translational degree-of-freedom (DOF), the first critical speed of the disk cannot increase more than the second critical speed of the original system (the disk with no constraint). The governing linear equations of transverse motion of a spinning disk with rigid body translational and tilting DOFs are used in the analysis of eigenvalues of the disk. The numerical solution of these equations is used to investigate the effect of the constraints on the critical speeds of the spinning disk. Experimental tests were conducted to verify the results.