Elastic interfacial waves in orthotropic interlayers.

Abstract

Elastic interfacial waves propagating along one of the planar boundaries separating an orthotropic interlayer of arbitrary uniform thickness from an orthotropic infinite surrounding solid are studied. The axes of material symmetry of the two materials are aligned with one of the axes coinciding with the propagation direction and another being perpendicular to the interfaces. The dispersion equation is derived in explicit form yielding the interfacial phase or group speed in terms of frequency, nondimensionalized with respect to the interlayer thickness, and the elastic constants and mass densities of the interlayer and the surrounding solid. Limiting cases of the dispersion equation give the secular equation for interfacial (Stoneley) waves in two semi‐infinite orthotropic materials and the frequency equation for an orthotropic plate. Analysis of the dispersion equation reveals several features. Under parameter conditions which are defined propagation at low frequencies cannot occur. Also material parameter combinations are found for which interfacial waves of arbitrary wavelength as compared to the interlayer thickness cannot propagate. Finally, the existence of standing waves as solutions of the bifurcation equation, a special case of the dispersion equation, is defined with respect to the parameters of the interlayer and the host material.