Shear-horizontal waves in a rotated Y-cut quartz plate with an isotropic elastic layer of finite thickness

We study shear-horizontal (SH) waves in a rotated Y-cut quartz plate carrying an isotropic elastic layer of finite thickness. The three-dimensional theories of anisotropic elasticity and isotropic elasticity are used for the quartz plate and the elastic layer, respectively. A transcendental frequency equation that determines the dispersion relations of the waves is obtained. The dispersion relations are obtained and plotted by solving the frequency equation using MATLAB. Approximate dispersion relations are also obtained analytically for two special cases. One is for long waves whose wavelength is much larger than the plate thickness. The other is for the case of a very thin elastic layer. The effects of the elastic layer on the dispersion relations are examined. The results obtained are fundamental and useful to acoustic wave sensors for measuring the mechanical and geometric properties of the elastic layer.