Elastic Guided Waves in a Pre-Stressed Compressible Layer Imbedded in a Pre-Stressed Two-Material Structure

Abstract

Abstract Elastic guided waves in a pre-stressed compressible layer imbedded in a pre-stressed two-material structure are examined. The waves propagate parallel to the planar layer interfaces as a superposed dynamic stress state on the statically pre-stressed layer. The stress condition in the layer and in the surrounding materials is arbitrary as are their strain energy functions. To gain understanding of the propagation characteristics, the mathematically tractable model of the materials having common principal axes of strain, one of which is perpendicular to the layering, is employed. The dispersion equation is derived in explicit form yielding guided wave phase and group speeds in terms of wavelength, stress and elastic parameters, and mass densities of the three materials. Limiting cases of the above dispersion equation give the dispersion equation of guided waves in a pre-stressed surface layer overlying a pre-stressed half space, the secular equation of interfacial waves in two semi-infinite pre-stressed materials, the secular equation of non-dispersive Rayleigh surface waves in a half-space, and the frequency equation of guided elastic waves in a pre-stressed compressible plate. Analysis of the dispersion equation reveals the propagation characteristics and their dependence on material and stress parameters. For small interlayer thickness the phase and group speeds are obtained in explicit form. This yields parameter conditions under which the structure acts as a mechanical filter to guided wave propagation. For arbitrary layer thickness, material parameter combinations are also found for which propagation cannot occur. Special attention is paid to the possible existence of interfacial standing waves as a limiting solution of the dispersion equation. Regions of material and stress parameters are defined in which standing waves exist. Numerical computations complement the analytical results for several classes of materials.