多孔陶瓷楔形樑之製備與彎曲振動分析

Preparation and Analysis on the Flexural Vibration of Porous Ceramic Tapered Beams

廖聖善(Sheng-Shan Liao)

指導教授 ： 蔡慧駿

淡江大學/工學院/機械與機電工程學系碩士班/碩士(2010年)

https://doi.org/10.6846/TKU.2010.01139

摘要

本研究以多孔氧化鋁楔形樑彎曲振動為主要研究方向。研究中將多孔氧化鋁樑之邊界條件設定為自由邊界與懸臂邊界限制。應用多孔樑有限元素頻域分析法，及聲響激振與衝擊激振試驗，探討多孔氧化鋁等截面樑與楔形樑之振動行為。由理論分析與實驗量測比較確立多孔彈性樑彎曲振動有限元素頻域分析之準確性。
　　研究中多孔氧化鋁樑係利用注漿成形法製作完成。成品經阿基米德法測得之通孔孔洞率皆於40%以上。透過掃描式電子顯微鏡觀察發現孔洞形狀近似圓形且孔洞分佈均勻，非常適合應用於含飽和流體多孔樑動態特性之研究。
　　由有限元素頻域分析與聲響及衝擊激振量測結果比較後發現，在自由邊界限制下，各組多孔氧化鋁樑之分析與量測模態頻率誤差皆小於4%。試驗中也發現，在懸臂邊界限制下若將楔形樑夾持端調緊會使模態頻率上升並降低誤差。但為避免施力過當造成多孔氧化鋁樑夾持端破裂，夾持時不易達到固定拘束，導致楔形樑分析與量測之模態頻率誤差稍微擴大，惟誤差值仍小於6%。此外分析與實驗量測獲得之模態亦幾近相符。顯示多孔彈性樑彎曲振動有限元素頻域分析，確可有效的應用於多孔氧化鋁楔形樑之彎曲振動分析上。

關鍵字

楔形樑 ； 彎曲振動 ； 多孔陶瓷 ； 氧化鋁

並列摘要

The main purpose of this study is to investigate the flexural vibration of porous ceramic tapered beam especially on that is made of alumina oxide (Al2O3). In the study, the boundary conditions considered for the porous alumina oxide tapered beams are free-free and clamped-free conditions. The porous beam finite element frequency-domain analysis and the acoustic as well as impact tests are applied to examine the vibration behaviors of porous beams with constant width and with uniform or linearly varying thickness. Through the comparisons of the analysis and experimental results, it is found that the proposed porous beam finite element frequency-domain analysis can accurately predict the flexural vibration behaviors of porous beams saturated with fluid.

　　In this study, the porous alumina oxide beams used are prepared by slip casting. The average porosity value of the beams measured by Archimedes method is found slightly above 40%. Through the scanning electron microscope examinations, it is also found that the pores are evenly distributed and have nearly circular cross-sectional shape. It can be concluded that the porous alumina oxide beams prepared for this study are suitable for the flexural vibration examinations of porous beam saturated with fluid.

　　After the comparisons of results obtained from the finite element frequency-domain analysis and the acoustic as well as impact tests, it is found that the percentage deviations of modal frequencies of free-free modes of every porous alumina oxide tapered beam examined are less than 4%. In the experiments, it is also learned that by increasing the clamping force on the clamped edge of a tapered beam will increase the modal frequencies measured and will also decrease the percentage deviations of modal frequencies of clamped-free modes. For preventing the rupture of the clamped edge caused by the excessive clamping force, an ideal clamped edge restraint cannot be easily achieved. Though the percentage deviations of modal frequencies of clamped-free modes obtained are slightly expanded, but still less than 6%. Moreover, the mode shapes obtained from the predictions and experiments are almost agreed. Above results showing that, the porous beam finite element frequency-domain analysis can be used to predict the flexural vibration behaviors of porous beams saturated with fluid and obtain accurate results.

並列關鍵字

Tapered Beam ； Flexural Vibration ； Porous Ceramic ； Alumina Oxide

參考文獻

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