表面微梁阵列对厚度剪切振动的石英谐振器共振频率的影响分析

发布时间：2018-05-08 16:44

本文选题：石英谐振器复合系统 + 微梁阵列　；参考：《华中科技大学》2015年硕士论文

【摘要】：本文建立了关于石英谐振器复合系统的二维动力学模型,其中,系统由石英晶体谐振器和表面微梁阵列构成。石英谐振器作厚度剪切振动,其基本方程按厚度剪切振动模式建立,而微梁的控制方程分别由欧拉-伯努利梁理论、铁摩辛柯梁理论和引入一阶应变梯度效应后的欧拉梁理论推导建立。在建立耦合动力学模型后,本文研究了表面微梁对石英谐振器共振频率的影响,并得到一些结论,最后对其物理意义进行了分析。分析发现:石英谐振器复合系统的共振频率会随着表面微梁的物理参数或者结构参数而呈现出周期性变化规律,并且相邻周期之间会有跳跃点出现。进一步模态分析发现,跳跃点两边的微梁振型的阶数发生改变,表明微梁与石英谐振器发生共振。对所得结果进行分析还可以看到,当附加微梁弹性模量增加到一定值时,频率漂移曲线中周期性消失。出现这种现象的原因是:固定其他参数时,当附加微梁的弹性模量增加到一定值之后,梁的一阶自振频率已经大于石英谐振器的振动频率,不会再有共振发生。而且随着弹性模量更进一步增大,表面微梁阵列对厚度剪切石英谐振器的作用逐渐趋近于与刚性质量层等效,这时的解可以由Sauerbrey方程求取。本文还通过所建立的耦合模型分析了微梁剪切变形对其与石英谐振器相互作用的影响,频率漂移曲线仍然呈现出周期性跳跃特征,与前面得到的结果进行比较分析可以看出,剪切变形对系统频率漂移存在一定影响,在高阶振动模态下,这种影响愈加明显。文章最后讨论了一阶应变梯度效应对所建立复合系统振动特性的影响,对得到的结果进行分析发现,应变梯度的引入将导致系统频率漂移曲线左移或者右移,并且随着应变梯度效应的增大,左移或右移效果愈加明显。出现这些现象的原因在于,应变梯度效应的引入增加了微梁的弯曲刚度。通过全文分析,能够更加了解复合石英谐振器系统的振动特性,得到的结果对其设计和频率稳定性分析都具有十分重要的意义。
[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.
【学位授予单位】：华中科技大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O73;TQ127.2

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