Abstract In this paper, propagation of Rayleigh surface wave in a compressible half-space solid with initial stress is discussed. The basic formulation of the problem includes the non linear theory of elasticity and theory of invariants. The equations governing infinitesimal motions superimposed on a finite deformation are used to study the combined effect of initial stress and finite deformation on wave speed. Secular equation governing the wave speed of a surface wave is presented and analyzed in detail. Various conditions are found for the existence and uniqueness of the wave speed. Furthermore, to understand the physical behavior of surface wave propagation, the theoretical results are plotted and analyzed for various numerical values of parameters involved in a prototype model. It is concluded that the surface wave speed is considerably affected by compression and tension as well as due to the stretch ratios of deformation. Moreover, for various choices of numerical values of governing parameters, the admissible numerical values of initial stress components and stretch ratios are also illustrated graphically.

中文翻译：

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瑞利波在初应力可压缩超弹性材料中的传播

摘要 本文讨论了瑞利面波在具有初始应力的可压缩半空间固体中的传播。该问题的基本表述包括非线性弹性理论和不变量理论。控制叠加在有限变形上的无穷小运动方程用于研究初始应力和有限变形对波速的综合影响。详细介绍并分析了控制表面波波速的长期方程。对于波速的存在性和唯一性，发现了各种条件。此外，为了了解表面波传播的物理行为，针对原型模型中涉及的各种参数数值绘制和分析理论结果。得出的结论是，表面波速度受压缩和拉伸以及变形拉伸比的影响很大。此外，对于各种控制参数数值的选择，初始应力分量和拉伸比的允许数值也有图形说明。