UBC Theses and Dissertations
Finite element analysis of rotating disks Nigh, Gregory Lynn
The finite element method is applied to the analysis of rotating disks. The equation governing the transverse deflection of a rotating disk is presented in both body-fixed and space-fixed coordinate systems. The quadratic stress triangle is used to determine the in-plane stress distribution which contributes to the out-of-plane stiffness. The out-of-plane problem is analyzed using elements based on the high precision 18 degree of freedom compatible plate bending triangle. Free vibration problems of both axisymmetric and non-axisymmetric disks are solved in the body-fixed coordinate system. The numerical results obtained for axisymmetric disks show good agreement with results from other analyses. In a space-fixed coordinate system, the response of a rotating axisymmetric disk to a space-fixed transverse load is examined in some detail. It is found that there exists a fundamental critical rotation speed at which a component of a natural vibration mode becomes stationary in space, leading to an instability. This critical speed may be related to a non-dimensional stiffness parameter which, together with the non-dimensional hub radius, completely defines the disk geometry and stiffness. Thus, it appears that the critical value of the stiffness parameter is a function only of the non-dimensional hub radius. The response of the disk past this critical stiffness is also examined. The results provide evidence of the existence of the higher critical speeds and indicate that the response is very sensitive to any approximations made with respect to the geometry of the disk or the in-plane stress distributions.
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