臺灣博碩士論文加值系統

旋轉圓盤在機械領域中使用非常廣泛，隨著精密機械時代的來臨，更凸顯旋轉圓盤角色的重要性，既有相關文獻，對於圓盤承受週期參數激振的研究卻不多見。
本文擬研究一圓盤承受定速旋轉的邊緣負荷之動態穩定性。在此研究中，依邊緣負荷為集中之共平面靜態力或週期力來探討。本文首先進行圓盤之應力分析，以決定因邊緣負荷所產生之應力分佈，再利用有限元素法得到離散化之系統運動方程式，而後利用模態分析法將耦合的運動方程式部分解耦化。最後以多尺度擾動法求得系統在各種不同之共振情況下之穩定邊界。
研究結果顯示，若邊緣負荷為靜態力，當作用力角度從徑向逐漸變成切線向時，不穩定區會隨之擴大。若邊緣負荷為週期力，作用力角度於 時系統最不穩定。

Rotating disks are widely used structural elements in various kinds of machinery. They are even more popular in modern ultra-precision machinery. However, studies of disks subjected to parametric excitations are very scarce in the existing literature .
This thesis presents a study of the dynamic stability of a stationary disk subjected spinning edge loads. The spinning edge loads are in-plane forces, which may be static or periodic in time. In this study, stress analysis is first conducted to determine the initial stresses caused by the edge loads. The finite element method is applied then to yield the discretized equations of motion. Finally, the method of multiple scales is adopted to determine the stability boundaries of the system.
From the results obtained, it is observed that if the edge loads are static force, unstable regions will exlarge with the angle between the force and the radial direction . When the edge loads are periodic forces, the system will be the most unstable as the angle of the loads is 45 .

目 錄
頁次
中文摘要…………………………………………………………….

英文摘要…..………………………………………………………... II
誌謝…………………………………………………………………. III
目錄……………………………………………………………….… IV
圖表索引……………………………………………………………. VI
第一章 緒論………………………………………………………... 1
1.1 前言………………………………………………………….. 1
1.2 文獻回顧…………………………………………………….. 2
1.3 研究動機與目的…………………………………………….. 6
第二章 理論分析………………………………………………….. 8
2.1圓盤受旋轉邊緣負荷之運動方程式………………………… 8
2.2圓盤之起始應力……………………………………………. 10
2.3有限元素法之離散化……………………………………….. 24
2.4模態分析……………………………………………………… 35
第三章 動態穩定性分析………………………………………….. 38
3.1靜態邊緣負荷………………………………………………… 38
3.2週期邊緣負荷………………………………………………… 46
第四章 數值分析與討論…………….……………………………. 57
4.1圓盤之自然頻率……………………………………….…… 57
4.2 圓盤承受旋轉靜態邊緣負荷之穩定性.…………………. . 58
4.3 圓盤承受旋轉週期邊緣負荷之穩定性.…………………. . 62
第五章 結論展望……………………………….…………………. 94
5.1結論…………………………………...…………………….. 94
5.2 未來展望………………………………...……………….... 95
參考文獻……………………………………………………………. 97
附錄A………………………………………………………………. 101

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