摘要
本研究理論利用BOND轉換矩陣(Bond Transformation Matrix)分別求出應力、應變轉換矩陣，再將此轉換矩陣進而推導出石英彈性對稱性、壓電性，將以上矩陣使用MATLAB數值分析軟體開發一套人機介面(Double_Rotational_Angle)程式，針對LC雙旋轉角切割角度，求得石英彈性、壓電、介電性係數矩陣，再將運算完之矩陣，在COMSOL Multiphysics有限元素分析軟體建立材料係數資料庫，分別模擬單一旋轉角3.8°、4.1°及雙旋轉角(YXwl) 11.17°/9.39°振動模態，由於單一旋轉角因切割角度差0.3°，在振動模態差異不大，振動都屬於對稱性，而雙旋轉角之振動呈現扭曲不對稱，故應用於精密感測元件易造成不良影響，故在發展雙旋角之切型，需針對不同需求去設計，才不會使得元件的壽命減短。 本研究藉由合作廠商的多片式切割機，製作LC雙旋轉角石英晶片，再利用X光測角儀，量測切割角度是否符合訂定角度，實驗結果發現因多片式切割機易造成石英晶片之表面平行度不佳，故未來若能以線切割機來精確的切割石英晶片，在角度控制的良率將有效的提升。
並列摘要
The applied theory in this thesis is Bond Transformation Matrix. It is applied to generate the stress and strain transformation matrix. I used the above mentioned matrix to derivate quartz’s symmetry. Then I combined the above mentioned matrix with the MATLAB to develop a GUI program: Doubly_Rotational_Angle. It can calculate elastic, piezoelectricity, dielectric matrices for quartz. After calculating, we build up quartz’s coefficients library in COMSOL Multiphysics .We use COMSOL to simulate the vibration modes of single-rotated-angled quartz at 3.8° and 4.1° individually and doubly-rotated-angled quartz at (YXwl) 11.16°/9.4°. Because the difference between single-rotated-angled quartz is only 0.3 degree, both of them have familiar symmetry. But doubly-rotated-angled quartz displays distortion and asymmetry. Therefore it is not recommended to apply to accurate sensor. In this thesis, I manufactured doubly-rotated-angled quartz with the multi-cutting machine supplied by collaborative company. Then I measured the cutting angle with x-ray goniometer. The result of this experiment shows that the quartz that was manufactured by multi-cutting machine is not parallel on its surface. In the future, we may use line-cutting machine to manufacture doubly-rotated-angled quartz to improve its surface accuracy.