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

[+] Author and Article Information
Ahmad Mohammadpanah

Department of Mechanical Engineering, the University of British Columbia, Vancouver, BC, Canada, V6T 1Z4FPInnovations, Vancouver, BC, Canada, V6T 1Z4

Stanley Hutton

Department of Mechanical Engineering, the University of British Columbia, Vancouver, BC, Canada, V6T 1Z4

1Corresponding author.

ASME doi:10.1115/1.4039421 History: Received July 15, 2017; Revised February 12, 2018


It can be predicted by Rayleigh’s interlacing eigenvalue theorem that structural modifications of a spinning disk can shift the 1st 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, 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 degrees of freedom 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.

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