The present paper articulates a mathematical model for the propagation of horizontally polarised shear (SH) wave in an initially stressed composite layered structure under the influence of an impulsive line source. The initially stressed composite structure is comprised of a transversely isotropic fluid saturated porous layer over a foundation with dry sandy elastic stratum and functionally graded substrate (semi-infinite medium) in which the bonding between the interfaces of the layers and semi-infinite medium are considered to be imperfect. Green's functions are derived for the composite layered structure by taking a line force/charge density (Dirac delta function) at the lower interface of intermediate stratum into the account. An efficient analytical treatment involving Green's function technique along with Fourier's transform has been employed to establish the closed form of dispersion equation for the propagating wave. As a special case of the problem, the closed form of dispersion equation has been deduced for a structure with a single layer overlying a semi-infinite medium. These deduced results are validated with pre-established results and classical Love wave equation. Numerical computation has been carried out to demonstrate graphically the effect of various affecting parameters, viz. wave number, initial stress, porosity, sandiness parameter, width ratio, imperfect bonding parameters and functional gradient parameters on the phase velocity of shear wave. Some remarkable results regarding the propagation behaviour of shear wave in the considered composite layered structure due to various affecting parameters serve as the major highlights of the present work which has significant relevance to field of geophysics, earthquake engineering and civil engineering.

本文阐述了一种在脉冲线源的影响下，在初始应力复合层状结构中水平极化剪切波（SH）传播的数学模型。初始受力复合结构由具有干砂弹性层的地基上的横观各向同性流体饱和多孔层和功能梯度基材（半无限介质）组成，其中考虑了各层与半无限介质之间的结合不完美。通过考虑中间层下部界面处的线力/电荷密度（狄拉克δ函数），得出复合层状结构的格林函数。涉及格林函数技术和傅立叶分析的有效分析处理 s变换已被用来为传播波建立色散方程的闭合形式。作为该问题的特例，已经推导了单层覆盖半无限介质的结构的色散方程的闭合形式。这些推论结果已通过预先建立的结果和经典的Love Wave方程进行了验证。进行了数值计算，以图形方式证明了各种影响参数的效果。波数，初始应力，孔隙度，含沙度参数，宽度比，不完美的粘结参数和功能梯度参数对剪切波的相速度。