Integral formalism for surface waves in piezoelectric crystals. Existence considerations

An integral formalism for surface waves in piezoelectric half‐infinite solids valid up to the critical velocity is developed. Various boundary conditions are considered and, in particular, the problem of which boundary conditions allow surface‐wave solutions for velocities below the limiting velocity vL is discussed in detail. It is proved that (a) with a mechanically free surface and zero dielectric constant for adjoining medium, at most one solution is possible for v<vL, (b) with a mechanically clamped surface and zero dielectric constant for adjoining medium, no solution is possible for v<vL, (c) with a mechanically clamped surface and an infinitely conducting adjoining medium, no solution is possible for v<vL, and (d) with a mechanically free surface and an infinitely conducting adjoining medium, at least one and at most two solutions are possible for v<vL. When two solutions are possible, one solution is of the Bluestein‐Gulyaev type.