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首页> 外文期刊>IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control >A unified formalism using effective surface permittivity to studyacoustic waves in various anisotropic and piezoelectric multilayers
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A unified formalism using effective surface permittivity to studyacoustic waves in various anisotropic and piezoelectric multilayers

机译：使用有效表面介电常数研究各种各向异性和压电多层中的声波的统一形式学

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摘要

A unified formalism is presented that uses the effective surfacenpermittivity (ESP) to study surface acoustic waves (SAW) in layerednsubstrates and guided waves in layered plates. Based on knownnmathematical tools, such as ordinary differential equation and transfernmatrix, a generalized surface impedance (GSI) concept is developed andnexploited to investigate the acoustic propagation in various anisotropicnand piezoelectric layered structures. The ESP function, originallyndefined for the surface of a homogeneous and semi-infinite piezoelectricnsubstrate, is extended to both the top surface of and an interface in anlayered half space, as well as to either surface of a finite-thicknessnplate. General ESP expressions for all mentioned configurations arenderived in terms of an equivalent GSI matrix. It is shown that, whennusing the appropriate GSI matrices, the same form of the ESP expressionsnapplies no matter whether the structure is a homogeneous half spacenalone or coated with a layered plate or a layered plate alone. GSInmatrices are explicitly given in terms of the bulk partial modensolutions for a substrate and via the transfer matrix for a plate.nModified GSI matrices for structures consisting of both a plate and ansubstrate are also specified. Analytical development is fully detailednto suit program implementation. To illustrate its versatility, thenformalism is also applied to two-substrate configurations, allowing onento analyze guided waves in a plate sandwiched between and interfacialnwaves existing along the boundary of two different media. Numericalnexamples are given to illustrate the spectrum features that the ESPnshows for various structures. Deduced ESP expressions allow one tonlocate directly all piezoelectrically active waves in any structurenincluding at feast one piezoelectric layer. Acoustic modes that are notnpiezoelectrically active and those in non-piezoelectric materials can benalso obtained by using the intermediate results, such as derived GSInmatrices
机译：提出了一种统一的形式主义，该形式主义使用有效的表面介电常数（ESP）研究分层n基底中的表面声波（SAW）和分层板中的导波。基于普通的微分方程和传递矩阵等已知的数学方法，开发并探索了广义表面阻抗（GSI）概念，以研究各种各向异性和压电层状结构中的声传播。 ESP功能最初是为均质和半无限压电基片的表面定义的，它不仅扩展到多层半空间的顶表面和界面，而且扩展到有限厚度板的任一表面。所有提及的配置的通用ESP表达式均以等效的GSI矩阵表示。结果表明，当使用适当的GSI矩阵时，无论结构是均质的半间隔材料还是单独涂覆分层板或单独分层板，都适用相同形式的ESP表达式。 GSInmatrices是根据基材的整体局部现代溶液以及通过板的传递矩阵明确给出的。还指定了由板和基材组成的结构的nGModified矩阵。分析开发已全面详述，以适合计划实施。为了说明其多功能性，然后将形式主义也应用于两个基板的配置，从而可以分析夹在两个波之间的板中的导波以及沿着两种不同介质的边界存在的界面波。给出了数值示例来说明ESPn显示的各种结构的光谱特征。推导的ESP表达式可以直接在任何结构上（包括至少一个压电层）直接定位所有压电有源波。通过使用中间结果（例如派生的GSInmatrices），还可以获取非压电活性和非压电材料中的声学模式。

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