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首页> 外文期刊>IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control >Analysis of 3-D vibrations of rectangular AT-cut quartz plates witha bi-mesa structure
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Analysis of 3-D vibrations of rectangular AT-cut quartz plates witha bi-mesa structure

机译：具有双台面结构的AT切割矩形石英板的3-D振动分析

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A method to analyze 3-D vibrations of rectangular AT-cut quartz,nbi-mesa-shaped plates is developed. The method is based on a classicalnapproach. As in 2-D analysis, the half structure of a plate is separatedninto a thick bi-mesa and a thin-side portion, and the displacement fieldnof each region is represented by a linear combination of guided waves.nIn the 3-D analysis, we apply the 2-D finite element method (FEM) tonobtain the waves guided by two pairs of parallel surfaces. Thenorthogonal property of guided modes is incorporated to approximatelynfulfil the continuity conditions at the interface between the thick andnthin portions. The stress-free conditions on the plate edges arensatisfied by employing the method of weighted residuals (MWR). Thencomputational advantage of this method is that it can greatly reduce thenmatrix size compared with the 3-D FEM. As a numerical example, thenfrequency spectra are calculated for X-elongated plates of bi-mesanshape, and the strong energy-trapping effect on the fundamentalnthickness-shear (TS) resonance is verified
机译：提出了一种分析矩形AT切割石英nbi-mesa形板的3-D振动的方法。该方法基于经典方法。与2-D分析中一样，将板的半结构分成厚的双台面和薄侧部分，每个区域的位移场n由导波的线性组合表示.n在3-D分析中，我们应用二维有限元方法（FEM）来获得由两对平行表面引导的波。引入了引导模态的正交特性，以大致满足厚壁部分和半壁部分之间的界面处的连续性条件。通过采用加权残差（MWR）的方法，可以满足板边缘无应力的条件。这种方法的计算优势在于，与3-D FEM相比，它可以大大减小矩阵尺寸。作为一个数值示例，然后计算了双介面形状的X伸长板的频谱，并验证了对基本厚度-剪切（TS）共振的强大能量俘获效应

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