The present paper investigates Green’s function technique to study the impact of the non-linear heterogeneity on the propagation of the horizontally polarised shear (SH) wave in a composite layered structure due to the line source. The composite structure is comprised of two distinct isotropic homogeneous elastic layers of finite width lying over an isotropic heterogeneous semi-infinite elastic medium. A general quadratic heterogeneity (including the linear heterogeneity term) in the rigidity of the semi-infinite medium has been taken into account. An efficient analytical treatment involving Green’s function technique along with the application of Fourier transformation has been employed to establish the closed form of the dispersion equation for the propagating wave. As a special case of the problem, the closed form of the dispersion equation has been found in well agreement with the pre-established and classical results. The influence of linear and non-linear heterogeneities on the phase velocity of the horizontally polarised shear-wave has been analysed comparatively for numerous cases associated with the considered model and the corresponding single layer half-space model. It is reported that the phase velocity of the horizontally polarised shear-wave is more pronounced in the case of the corresponding single layer half-space structure as compared to the considered structure. Also, the impact of the general quadratic heterogeneity (supported by the linear heterogeneity) enhances the phase velocity most favourably as compared to the case of the simple quadratic heterogeneity, linear heterogeneity and homogeneity in the semi-infinite medium.

中文翻译：

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格林函数技术研究复合层状结构中线源引起的非均质性对水平极化剪切波传播的影响

本文研究格林函数技术，以研究非线性异质性对线源引起的复合层状结构中水平极化剪切波（SH）传播的影响。复合结构由位于各向同性异质半无限弹性介质上的有限宽度的两个不同的各向同性均质弹性层组成。已经考虑了半无限介质刚度上一般的二次异质性（包括线性异质性项）。一种有效的分析方法，包括格林函数技术以及傅里叶变换的应用，已被用来建立传播波色散方程的封闭形式。作为问题的特例，已经发现色散方程的闭合形式与预先建立的经典结果非常吻合。对于与所考虑的模型和相应的单层半空间模型有关的许多情况，已经比较分析了线性和非线性非均质性对水平极化切波的相速度的影响。据报道，与所考虑的结构相比，在相应的单层半空间结构的情况下，水平极化剪切波的相速度更加明显。而且，与半无限介质中简单的二次异质性，线性异质性和均质性的情况相比，一般的二次异质性（由线性异质性支持）的影响最有利地提高了相速度。