Influence of viscosity on the motion of quasi-particles associated with surface acoustic waves

Selecting this case as a tractable example, this work constructs an original quasi-particle mechanics associated with the dissipative continuum wave solution of so-called Bleustein–Gulyaev (BG) surface acoustic waves (SAWs). These propagate along an elastic semi-infinite space of appropriate crystalline symmetry allowing for the existence of a pure shear-horizontal (SH) displacement but with small viscosity treated as a perturbation. This association is built through the consideration of the canonical conservation (or non-conservation) of energy and wave momentum integrated over a material volume representative of the wave process in the presence of viscous dissipation. At the considered order of approximation, the resulting point mechanics is that of a quasi-particle moving at constant velocity (equal to that of the non-viscous case), but the motion is no longer inertial – due to viscosity – exhibiting a varying “mass” in time, in fact decreasing during the progress of the wave through the viscous material. This “mass” is characteristic of the amplitude of the wave signal, of the behavior of the wave in depth in the substrate, of the present electromechanical coupling, and of the boundary conditions assumed at the top surface, here enriched by the viscous effect. The mechanics obtained reminds us of the Leibnizian “vis-viva”, when the energy variation is considered.