液體耦合圓形壓電層板之振動分析

Abstract

本研究以實驗量測及數值模擬探討液體耦合壓電陶瓷層板的振動特性，以夾具將壓電蜂鳴片水平或垂直固定，與液體耦合。耦合液體的附加質量及結構阻尼是蜂鳴片頻率漂移的主要原因，將實驗數據與ANSYS模擬結果比較，證明這二種效應的貢獻。 數值模擬以ANSYS套裝軟體求得共振頻率與模態，未考慮結構阻尼效應的數值結果發現隨著注水量的增加，蜂鳴片的共振頻率逐漸向低頻漂移。當水的液面高度接近10mm時，共振頻率的變化慢慢趨緩，蜂鳴片垂直或水平置放的共振頻率變化大致相似，顯示附加質量的影響有一定限度。 實驗以SigLab動態頻譜分析儀量測蜂鳴片的共振頻率，比較實驗值與模擬值，二者的數值及趨勢皆相似。結構阻尼係透過比例阻尼原理，由試片的頻率響應計算出質量阻尼常數及勁度阻尼常數，代入ANSYS，模擬阻尼效應對共振頻率的影響，結果顯示隨著液面高度的增加，共振頻率降低，其變化量相對於附加質量的影響明顯較低。在敏感度較低的條件中，甚至可以忽略阻尼效應造成的頻率變化。附加質量之模擬值較實驗值低，若考量液體重量及壓力，造成蜂鳴片承受徑向拉應力，模擬值與實驗值將更為相符。

A coordinated experimental and numerical investigation of vibration characteristics of liquid coupled circular piezoelectric laminates is presented in this thesis. The circular piezoelectric buzzers clamped at their borders in horizontal and vertical set-ups, respectively, are loaded by liquid on one side. Resonant frequencies of the buzzer immersed in liquid are usually reduced to lower values than those measured in its free state. The contributions due to both adding mass of liquid and structural damping are verified through experiments and simulation carried out by ANSYS commercial code. Resonant frequencies and their corresponding natural modes of the buzzer which is free of damping were determined first by ANSYS. Numerical result reveals that the difference between resonant frequencies of free buzzer and the one immersed in water tends to monotonically decrease with the increase of liquid level in either vertical or horizontal set-up. The addition of liquid to the buzzer has significant influence on the drifts of resonant frequencies. The variation becomes a constant if liquid layer approaches a limited thickness. Resonant frequencies were measured by use of a SigLab spectrum analyzer in experiments. The measured values have the same trends as numerical results. Based on hypothesis of proportional damping, the damping factors related to mass and stiffness are determined through measurement. The influence of structural damping is much less than adding mass in simulation by ANSIS. The contribution of structural damping can be ignored in most cases. The simulated resonant frequencies are lower than measured ones. The agreement can be remedied if hydrostatic pressure-induced radial pre-stress is included in calculating resonant frequency values of the buzzer.