Abstract: The dispersion equation for quasi-Rayleigh acoustic modes in transversely isotropic sandwich-type structures (an elastic layer between two substrates) has been obtained in the analytical form. The equation is analyzed for three types of structures—a layer between two soft substrates, a layer between a soft and a hard substrate, and a structure consisting of two contacting substrates with markedly different values of hardness. Eigenmodes are determined for all three structures. Depending on the combination of the material parameters in these structures, these eigenwaves are either Rayleigh-type waves localized at interfaces in the substrates and accompanying a Lamb wave in the interlayer (in the absence of an interlayer, forming a Stoneley wave) or the leaky modes characterized by a small imaginary addition to the phase velocity and the presence of bulk partial waves of leakage providing some energy removal from the interfaces. Without any calculations, simple criteria were established that allow one to predict the existence of a leaky mode in the given structure and the number of leakage fluxes it contains. The resonance reflection is analized for the case where the incidence angle of the wave in the substrate corresponding to the velocity v of the wave-front propagation along the interface is close to the value of the real part of the phase velocity of the leaky mode.
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