Axisymmetrical Snapping of Spinning Nonflat Disks
Date Issued
2004
Date
2004
Author(s)
Lin, Chih-Chung
DOI
en-US
Abstract
In this paper we study the steady state deflection of a spinning nonflat disk, both theoretically and experimentally. The initial and the deformed shapes of the disk are assumed to be axisymmetrical. Von Karman’s plate model is adopted to formulate the equations of motion, and Galerkin’s method is employed to discretize the equations. In the case when the initial height of the non-flat disk is sufficiently large, multiple equilibrium positions can exist, among them the two stable one-mode solutions and are of particular interest. Theoretical investigation shows that if the disk is initially in the stressed position , it will be snapped to position when the rotation speed reaches a critical value. Experiments on a series of copper disks with different initial heights are conducted to verify the theoretical predictions. Generally speaking, the experimental measurements agree very well with theoretical predictions when the initial height is small. For the disks with large initial height, on the other hand, the real snapping speeds are significantly below the theoretical predictions. The circumferential waviness of the copper disks induced inevitably in the manufacturing process and the aerodynamic forces at high rotation speed are two possible factors causing this discrepancy.
Subjects
離散化
軸對稱挫曲
discretize
Axisymmetrical Snapping
Type
thesis
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