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題名 | 石英音叉諧振器頻率分析=The Frequency Analysis of Tuning Fork Quartz Resonators |
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作者姓名(中文) | 謝發華; | 書刊名 | 新新科技年刊 |
卷期 | 11 2015.01[民104.01] |
頁次 | 頁60-71 |
分類號 | 446 |
關鍵詞 | 石英音叉; 非等向性勁度; 漢米爾頓原理; 自然頻率; Quartz tuning fork; Anisotropic stiffness; Hamilton's principle; Resonance frequency; |
語文 | 中文(Chinese) |
中文摘要 | 本研究對於石英音叉諧振器先拆解成懸臂樑與緩衝塊,並分別建構合理位移場,以運用漢米爾頓原理列出包含壓電效應的動能與電焓,再以變分法建立統御方程式與邊界條件、以及使用分離變數法求得特徵方程式、並解出特徵值等程序,最後將懸臂樑與緩衝塊耦合,以獲得自由振動數學模型,成功地建立石英音叉諧振器頻率解析解模型。 |
英文摘要 | The resonant frequencies of tuning fork quartz resonator are analyzed. The structure is made of Z-cut quartz wafers, which are anisotropic in elastic stiffness, dielectric and piezoelectric constants. With the proof mass included more additional modes, such as antiphase modes, are created. In anti-phase bending mode the two parallel beams vibrate in opposite directions. It is easy to model the deformation of the two slender beams, but difficult to model that of the proof mass. The deformation model of the proof mass is proposed so that the mode shapes and natural frequencies can be solved exactly based on the equations of motion derived from the Hamilton's principle. The theoretically-obtained natural frequency is compared with the experimental one. |
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