半雙曲線近似對含裂紋之壓電材料動態特性影響之研究

Investigation of Effects on Dynamic Characteristics for Cracked Piezoelectric Materials due to Quasi-hyperbolic Approximation

謝友誌(Yu-Chih Hsieh)

指導教授 ： 應宜雄

淡江大學/工學院/航空太空工程學系碩士班/碩士(2007年)

https://doi.org/10.6846/TKU.2007.00257

摘要

本文利用半雙曲線近似下推導而得的線彈性壓電控制方程式與本構方程式，解析一含有限長裂紋之無窮域壓電材料，於裂紋面上施加反平面應力及平面電位移的簡諧載荷問題。此外，本文亦將此假設應用於靜力問題上，解析一含有限長Yoffe擴展裂紋之壓電材料，於無窮遠處施加反平面應力及平面電位移負載之靜態力問題。本文利用積分轉換法求得含裂紋之壓電材料分別受簡諧載荷與靜力負載時的解析解，並與穩靜態近似下所得到之解作比較。最後針對所求之應力強度因子振幅大小以及相位，做詳細的數值計算與討論。

關鍵字

半雙曲線近似 ； 壓電材料 ； 振動 ； 裂紋 ； 應力強度因子

並列摘要

In this study, the quasi-hyperbolic approximation is used to investigate the dynamic behavior of a crack under the action of anti-plane stresses and in-plane electric displacements in a piezoelectric material. First, the steady-state response of a finite crack subjected to harmonically anti-plane loading and in-plane electric displacement on crack faces is analyzed. Moreover, a moving crack of Yoffe type in piezoelectric materials under remote anti-plane static stresses and in-plane static electric displacements is studied. The stress intensity factors and electric displacement intensity factors are obtained for both problems. Finally, numerical results of the first problem are evaluated and discussed in detail.

並列關鍵字

quasi-hyperbolic approximation ； piezoelectric ； vibration ； crack ； stress intensity factor

參考文獻

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