不同邊界條件矩形平板之振動分析

Vibration analysis of rectangular plates with the different boundary conditions

鄭郁翰(Yun-Han Chung)

指導教授 ： 孫書煌 ； 何星輝

崑山科技大學/工程學院/機械工程研究所/碩士(2006年)

摘要

在生活週遭隨處可見振動的產生，因此振動問題的改善都相當受到重視，而想改善問題必先量測目標物的結構共振頻率。而共振頻率問題是動態機械或結構所面臨的重要問題，在共振頻率下所產生之大振幅常為機械或結構破壞的主因。本文將深入探討矩形平板在不同邊界條件的狀態下，對結構振動行為的影響。
本文採用有限元素分析(Finite Element Analysis)，應用ANSYS與實驗方法相互探討，研究不同邊界條件下矩形平板的振動問題，分別以自由（Free）邊界、簡支撐(Simply Supported)與固定(Clamped）邊界為基礎探討。利用不同材質，如：棉繩、海棉、橡皮筋與氣球對自由邊界進行模擬，尋求最佳結果。簡支撐的部份，則是以剛性較軟之材質進行模擬。而固定邊界則用楔形塊夾持，以模擬固定邊界情況。從實驗模擬與有限元素分析做進一步的結合，以解決結構之共振問題

關鍵字

有限元素分析 ； 不同邊界條件 ； 共振頻率 ； 自然頻率 ； 矩形平板

並列摘要

Vibration happens everywhere surrounding the real world. How to reduce vibration damages, therefore, is an important issue. Most vibration damages results from resonance, and resonance results from the operating frequency being too close structure nature frequency. As a result, obtain structure nature frequency is essential in reducing vibration damages.
In this thesis, the vibration of a rectangular plate with different boundary conditions (BC) is evaluated. A real rectangular plate is experimented under free, simple supported and clamped BC. The vibration frequency and mode are measured from B&K hardware. The same situations are also simulated in ANSYS, a powerful CAE software. The simulating results can be verified with the results from experiments. The cotton line, foam rubber, rubber band, balloon is used as the support, and evaluated to find which one can approximate the free BC best. A softer material is used in simple supported case and a wedge is used in clamped case.

並列關鍵字

Finite Element Analysis ； Different boundary conditions ； Resonance frequency ； Natural frequency ； ANSYS ； Rectangular plates

參考文獻

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[12] Leissa, A. W., “The Free Vibration of Rectangular Plates,” Journal of Sound and Vibration, Vol. 31, No. 3, 1973, pp. 257-293.