Dimitrios A. Sotiropoulos
Dept. of Eng. Sci., Tech. Univ. of Crete, Chania 73100, Greece
Christoforos G. Sifniotopoulos
Northwestern Univ., Evanston, IL 60208
Propagating and standing interfacial waves between a surface layer and an underlying half-space, both under finite strain, are examined. The media are compressible nonlinear elastic and homogeneously pre-strained with their principal axes of pre-strain aligned, one axis being normal to the planar interface. For arbitrary strain energy functions and propagation along a principal axis of pre-strain, the dispersion equation is obtained. A low-frequency wave speed is subsequently obtained in explicit form yielding nonpropagation parameter conditions which for a specific state of stress hold at any frequency. The high-frequency limit of the dispersion equation yields the secular equation for interfacial waves between two half-spaces. It is then found that equal-density compressible materials may allow propagation and that compressible materials with equal shear wave velocities parallel to the interface may filter interfacial waves, even under isotropic in-plane stretching. For an arbitrary layer thickness as compared to the wavelength, material and pre-strain parameter conditions are also derived for the existence of standing waves as solutions of the bifurcation equation, a limiting case of the dispersion equation.