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首页> 外文期刊>IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control >Boundary integral equations from Hamilton's principle for surface acoustic waves under periodic metal gratings
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Boundary integral equations from Hamilton's principle for surface acoustic waves under periodic metal gratings

机译：周期性金属光栅下表面声波的哈密顿原理的边界积分方程

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摘要

The procedure describes the derivation of boundary integral equations for surface acoustic waves propagating under periodic metal strip gratings with piezoelectric films. It takes into account the electrical and mechanical perturbations, including the effects of mass loading caused by the gratings with an arbitrary shape. First, an integral equation is derived with line integrals on the boundaries within one period. This derivation is based on Hamilton's principle and uses Lagrange's method of multipliers to alleviate the continuous conditions of the displacement and the electric potential on the boundaries. Second, boundary integral equations corresponding to each substrate, piezoelectric film, metal strip, and free space region are obtained from the integral equation using the Rayleigh-Ritz method for admissible functions. With this procedure, it is not necessary to make any assumptions for separation of the boundary conditions between two neighboring regions. Consequently, we clarify the theoretical basis for the analytical procedure using boundary integral equations for longitudinal LSAW modes.
机译：该程序描述了在带有压电膜的周期性金属带光栅下传播的表面声波的边界积分方程的推导。它考虑了电气和机械扰动，包括由任意形状的光栅引起的质量负载的影响。首先，在一个周期内边界上的线积分得到一个积分方程。该推导基于汉密尔顿原理，并使用拉格朗日乘数法来缓解位移的连续条件和边界上的电势。其次，使用Rayleigh-Ritz方法针对允许函数，从积分方程中获得与每个基板，压电膜，金属带和自由空间区域相对应的边界积分方程。利用该程序，不必对两个相邻区域之间的边界条件的分离进行任何假设。因此，我们阐明了使用边界积分方程求解纵向LSAW模式的分析程序的理论基础。

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