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Title: | 圓板在重力作用下靜態與旋轉的非對稱變形 Warping of Stationary and Rotating Heavy Disks |
Authors: | Yao-Yi Fang 方耀億 |
Advisor: | 陳振山(Jen-San Chen) |
Keyword: | 重力下圓板,非軸對稱變形,von Karman平板理論,空氣擾動, Heavy disk,Non-axisymmetric warping,Aeroelastic flutter, |
Publication Year : | 2011 |
Degree: | 碩士 |
Abstract: | 於本文將探討圓板在外徑不受拘束、內徑被夾持下受到重力作用的非軸對稱變形。理論上以von Karman平板理論推導出旋轉圓板在重力作用下的運動方程式;實驗上使用5.25吋軟式磁碟片來觀察靜態及旋轉時圓板的非軸對稱變形。我們先量測磁碟片在靜態時的變形,當夾持部份的半徑與圓板半徑的比值為0.3時,可發現在重力作用下碟片會有兩種非軸對稱的變形同時存在,分別為cos2θ及cos3θ的形狀。在夾持部份的半徑與圓板半徑的比值維持0.3的情況下,我們讓碟片開始旋轉,若碟片從靜態的cos2θ變形開始增加轉速,在轉速達303 rpm時可觀察到變形變為cos3θ的形狀,且一直持續到轉速增加至1010 rpm;1010 rpm時,碟片變為軸對稱的變形;當轉速達到1313 rpm之後,空氣造成的擾動會使碟片的變形無法到達穩態。將碟片從高轉速逐漸降低轉速回到靜態後,可觀察到變形仍然維持cos3θ的形狀,而非變回一開始的cos2θ。在靜態時同時存在兩種非軸對稱變形及旋轉時的變形變化都與理論的預測ㄧ致。 A flexible circular plate with gravity as its main source of external loading is called a heavy disk. This paper studies the non-axisymmetric warping of a clamped-free heavy disk. In the theoretical formulation, von Karman’s plate model is adopted to derive the equations of motion of a rotating heavy disk. In the experiment, a 5.25-inch floppy disk is used to demonstrate the non-axisymmetric deformations when the disk is either stationary or rotating. We first measured the shape of the floppy disk when it was stationary. It was observed that two non-axisymmetric deformations coexisted, one with shape cos2θ and the other cos3θ. We next rotated the floppy disk. It was observed that when the floppy disk started with shape cos2θ, the deformation switched to shape cos3θ as the rotation speed increased to 303 rpm. As the speed continued to increase, the shape cos3θ persisted all the way up to 1010 rpm. Beyond that the disk deformation became axisymmetric until 1313 rpm. Beyond 1313 rpm, aeroelastic flutter started to kick in and steady state was no longer achievable. The rotation speed was then reduced gradually from high speed to 0. It was found that the deformation remained cos3θ all the way, instead of switching back to the cos2θ shape the disk started out with in the first place. The coexistence of two stable non-axisymmetric deformations of the stationary disk and the hysteresis behavior of the rotating disk observed in the experiment are consistent with theoretical predictions. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/23690 |
Fulltext Rights: | 未授權 |
Appears in Collections: | 機械工程學系 |
Files in This Item:
File | Size | Format | |
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ntu-100-1.pdf Restricted Access | 2.82 MB | Adobe PDF |
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