本文選題：石英諧振器復合系統(tǒng) + 微梁陣列��； 參考：《華中科技大學》2015年碩士論文

【摘要】：本文建立了關于石英諧振器復合系統(tǒng)的二維動力學模型,其中,系統(tǒng)由石英晶體諧振器和表面微梁陣列構成。石英諧振器作厚度剪切振動,其基本方程按厚度剪切振動模式建立,而微梁的控制方程分別由歐拉-伯努利梁理論、鐵摩辛柯梁理論和引入一階應變梯度效應后的歐拉梁理論推導建立。在建立耦合動力學模型后,本文研究了表面微梁對石英諧振器共振頻率的影響,并得到一些結論,最后對其物理意義進行了分析。分析發(fā)現(xiàn):石英諧振器復合系統(tǒng)的共振頻率會隨著表面微梁的物理參數(shù)或者結構參數(shù)而呈現(xiàn)出周期性變化規(guī)律,并且相鄰周期之間會有跳躍點出現(xiàn)。進一步模態(tài)分析發(fā)現(xiàn),跳躍點兩邊的微梁振型的階數(shù)發(fā)生改變,表明微梁與石英諧振器發(fā)生共振。對所得結果進行分析還可以看到,當附加微梁彈性模量增加到一定值時,頻率漂移曲線中周期性消失。出現(xiàn)這種現(xiàn)象的原因是:固定其他參數(shù)時,當附加微梁的彈性模量增加到一定值之后,梁的一階自振頻率已經(jīng)大于石英諧振器的振動頻率,不會再有共振發(fā)生。而且隨著彈性模量更進一步增大,表面微梁陣列對厚度剪切石英諧振器的作用逐漸趨近于與剛性質(zhì)量層等效,這時的解可以由Sauerbrey方程求取。本文還通過所建立的耦合模型分析了微梁剪切變形對其與石英諧振器相互作用的影響,頻率漂移曲線仍然呈現(xiàn)出周期性跳躍特征,與前面得到的結果進行比較分析可以看出,剪切變形對系統(tǒng)頻率漂移存在一定影響,在高階振動模態(tài)下,這種影響愈加明顯。文章最后討論了一階應變梯度效應對所建立復合系統(tǒng)振動特性的影響,對得到的結果進行分析發(fā)現(xiàn),應變梯度的引入將導致系統(tǒng)頻率漂移曲線左移或者右移,并且隨著應變梯度效應的增大,左移或右移效果愈加明顯。出現(xiàn)這些現(xiàn)象的原因在于,應變梯度效應的引入增加了微梁的彎曲剛度。通過全文分析,能夠更加了解復合石英諧振器系統(tǒng)的振動特性,得到的結果對其設計和頻率穩(wěn)定性分析都具有十分重要的意義。
[Abstract]:In this paper, a two-dimensional dynamic model of a quartz resonator composite system is established. The system consists of a quartz crystal resonator and a surface microbeam array. The basic equation of quartz resonator is established according to the mode of thickness shear vibration, and the control equation of micro-beam is derived from Euler-Bernoulli beam theory, respectively. The theory of Te-Moxinko beam and the theory of Euler beam after introducing the first order strain gradient effect are established. After the coupling kinetic model is established, the effect of surface microbeam on the resonance frequency of quartz resonator is studied, and some conclusions are obtained. Finally, the physical meaning of the model is analyzed. It is found that the resonance frequency of the quartz resonator composite system changes periodically with the physical or structural parameters of the surface microbeam, and there are jump points between adjacent periods. Further modal analysis shows that the order of mode shapes of the microbeams on both sides of the jump point is changed, which indicates that the microbeam resonates with the quartz resonator. It can also be seen that when the elastic modulus of the additional micro-beam increases to a certain value, the frequency drift curve disappears periodically. The reason for this phenomenon is that when other parameters are fixed, when the elastic modulus of the additional micro-beam is increased to a certain value, the first order natural frequency of the beam is already larger than that of the quartz resonator, and no resonance will occur again. With the further increase of the elastic modulus, the effect of the surface microbeam array on the thickness shear quartz resonator is gradually approaching to be equivalent to the rigid mass layer. The solution can be obtained from the Sauerbrey equation. The effect of shear deformation on the interaction between microbeam and quartz resonator is also analyzed by the coupling model. The frequency drift curve still shows the characteristic of periodic jump, and compared with the results obtained before, it can be seen that the frequency drift curve has the characteristics of periodic jump. The shear deformation has a certain influence on the frequency drift of the system, and the effect is more obvious under the higher vibration mode. Finally, the influence of the first order strain gradient effect on the vibration characteristics of the composite system is discussed. It is found that the introduction of the strain gradient will lead to the left or right shift of the frequency drift curve of the system. With the increase of strain gradient effect, the effect of left or right shift becomes more obvious. The reason for these phenomena is that the introduction of strain gradient effect increases the bending stiffness of the micro beam. Through the full text analysis, the vibration characteristics of the composite quartz resonator system can be better understood. The results obtained are of great significance for its design and frequency stability analysis.
【學位授予單位】：華中科技大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：O73;TQ127.2

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