石英晶体板非线性高频振动的拓展伽辽金法分析

摘要/Abstract

摘要： 针对考虑几何和材料非线性的石英晶体板厚度剪切振动和弯曲振动的方程组,利用扩展伽辽金法对该方程组进行转化和求解,分别获得了强烈耦合的厚度剪切振动模态和弯曲振动模态的频率响应关系,绘制了不同振幅比和不同驱动电压影响下的频率响应曲线图。数值计算结果表明可以选取石英晶片的最佳长厚比尺寸来避免两种模态的强烈耦合。驱动电压的变化将引起石英晶体谐振器厚度剪切振动频率的明显改变,必须将振动频率的漂移值控制在常用压电声波器件的允许值之内。扩展伽辽金法对石英晶体板非线性振动方程组的求解为非线性有限元分析和偏场效应分析奠定了基础。

关键词: 石英晶体板, 非线性振动, 频率, 拓展伽辽金法, 有限元分析

Abstract: For the nonlinear equations of thickness-shear vibration and flexural vibration of quartz crystal plate considering geometric and material nonlinearity, the equations are transformed and solved by the newly proposed extended Galerkin method. The strongly coupled frequency-response relationships of thickness-shear and flexural vibrations of quartz crystal plate are obtained respectively, and the frequency-response curves under the influence of different amplitude ratios and different driving voltages are drawn. The numerical results show that the optimal aspect ratio size of quartz wafer should be selected to avoid the strong coupling of the two modes. The change of driving voltage will cause the obvious change of thickness-shear vibration frequency of quartz crystal resonator. The frequency shift value must be controlled within the allowable value of common piezoelectric acoustic devices. The solution of high frequency nonlinear vibration equations of quartz crystal plate by extended Galerkin method lays a foundation for nonlinear finite element analysis and partial field effect analysis.

Key words: quartz crystal plate, nonlinear vibration, frequency, extended Galerkin method, finite element analysis

中图分类号:

TH123⁺.1

吴荣兴, 王晓明, 张青艳, 王骥. 石英晶体板非线性高频振动的拓展伽辽金法分析[J]. 人工晶体学报, 2022, 51(8): 1431-1436.

WU Rongxing, WANG Xiaoming, ZHANG Qingyan, WANG Ji. Analysis of Nonlinear High Frequency Vibrations of Quartz Crystal Plate with Extended Galerkin Method[J]. JOURNAL OF SYNTHETIC CRYSTALS, 2022, 51(8): 1431-1436.

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