硅酸镓镧晶体谐振器的高频振动分析  

Analysis of high frequency vibrations of La_(3)Ga_(5)SiO_(14)crystal resonator

作　　者：吴荣兴[1,2] 王晓明 唐忠平 王骥[2] WU Rongxing;WANG Xiaoming;TANG Zhongping;WANG Ji(Institute of Applied Mechanics,Ningbo Polytechnic,Ningbo 315800,Zhejiang,China;School of Mechanical Engineering and Mechanics,Ningbo University,Ningbo 315211,Zhejiang,China)

机构地区：[1]宁波职业技术学院应用力学研究所,浙江宁波315800 [2]宁波大学机械与力学学院,浙江宁波315211

出　　处：《声学技术》2023年第6期852-856,共5页Technical Acoustics

基　　金：2021年宁波职业技术学院研究机构专项课题"考虑复杂结构的石英晶体谐振器分析"(NZ21JG007)。

摘　　要：利用Mindlin板理论分析了硅酸镓镧晶体板强耦合的厚度剪切振动和弯曲振动,获得了硅酸镓镧晶体板高频振动的色散关系、频谱关系和振动模态位移图。数值计算结果表明,Mindlin板理论可以获得硅酸镓镧晶体板厚度剪切振动的一阶精确截止频率,无需修正系数。基于石英晶体谐振器设计晶片最佳长厚比的选取方法,确定了硅酸镓镧晶片的最佳尺寸,避免了厚度剪切振动模态和弯曲振动模态的强耦合。通过绘制硅酸镓镧晶体板在最佳尺寸时的各振动模态位移图,发现厚度剪切振动模态是主振模态,具有很好的能陷效应。Mindlin板理论在硅酸镓镧晶体板高频振动的应用分析可以指导硅酸镓镧晶体谐振器的实际研发。The strong coupled thickness-shear vibration and flexural vibration of the La_(3)Ga_(5)SiO_(14)crystal plate are analyzed with Mindlin plate theory,and the dispersion relationships,spectrum relationships and vibration mode displacements of high frequency vibrations of La_(3)Ga_(5)SiO_(14)crystal plate are obtained.The numerical results show that the first-order accurate cut-off frequency of thickness-shear vibrations of La_(3)Ga_(5)SiO_(14)crystal plate can be obtained with the Mindlin plate theory without correction coefficients.According to the selection method of the optimal length/thickness ratio of chip design chip of the quartz crystal resonator,the optimal size of La_(3)Ga_(5)SiO_(14)crystal wafer is determined to avoid the strong coupling bteween thickness-shear vibration mode and flexural vibration mode.By drawing the displacement diagrams of each vibration mode with the optimal size of La_(3)Ga_(5)SiO_(14)crystal plate,it is found that the thickness-shear vibration mode is the main vibration mode with a good energy trapping effect.The application and analysis of Mindlin plate theory in the high frequency vibration of La_(3)Ga_(5)SiO_(14)crystal plate can guide the practical research and development of La_(3)Ga_(5)SiO_(14)crystal resonator.

关 键 词：硅酸镓镧晶体 振动 频率 厚度剪切 谐振器 

分 类 号：TP12[自动化与计算机技术—控制理论与控制工程]