Layer guided shear horizontally polarized acoustic plate modes

Abstract

The theoretical basis describing Love waves propagating on a finite thickness substrate covered by a finite thickness solid layer having a lower shear acoustic speed is considered. A generalized dispersion equation is derived for shear horizontally polarized acoustic waves in this system. Two types of solutions to the dispersion equation, both satisfying stress free boundary conditions at the free surfaces, are shown to exist. The first type of solution has a displacement that decays with depth into the substrate while the second does not. Analytical approximations to the solutions for a thin solid guiding layer show that these solutions can be considered as generalizations of Love waves and resonant shear horizontally polarized acoustic plate modes (SH-APM), respectively. Numerical solutions to the dispersion equation are developed and the spectrum of modes for thick guiding layers is examined with particular reference to sensor applications. As expected, increasing the thickness of the guiding layer leads to multiple Love wave modes. However, each of these Love wave modes is found to possess a set of shear horizontally polarized acoustic plate modes. As the guiding layer thickness is increased, the Love wave speed decreases until at approximately νl/4f, where νl is the shear acoustic speed of the layer and f is the frequency, a sharp transition occurs in the Love wave speed from a value close to the shear acoustic speed of the substrate, νs, to one close to the shear acoustic speed of the layer, νl. A similar pattern is observed for the layer guided SH-APM’s with an increase in the guiding layer thickness resulting in a sharp transition in the speed of the SH-APM towards a value close to that of the next lower SH-APM. It is shown that the appearance of the second Love wave mode is a result of a continuation of the lowest SH-APM associated with the previous Love wave mode. A physical interpretation is developed for the Love waves on the finite substrate and for the layer guided SH-APM’s and from this interpretation it is suggested that layer guided SH-APM sensors could provide significantly enhanced mass sensitivity.