Sensitivity of Love surface waves to mass loading

Abstract

The sensitivity of the phase velocity vp of Love surface waves to mass loading is a very important characteristic of Love wave devices. In this paper, we present a novel approach to evaluate the sensitivity of Love surface waves to loading with an infinitesimal layer of mass of a surface density σkg/m2. To this end, the we developed analytical formulas for the mass coefficient of sensitivity Sσvp=(1/vp)dvp/dσ [m2/kg] and phase velocity gradients −dvp(f)/df and −dvp(h1)/dh1, where f and h1 stand, respectively, for frequency of the Love wave and thickness of the guiding surface layer. We also established analytical formulas that relate the mass sensitivity Sσvp with 1) the relative slope (gradient) −(1/vp)dvp/dh1 of the phase velocity dispersion curve vp(h1), and 2) the relative slope (gradient) −(1/vp)dvp/df of the phase velocity dispersion curve vp(f). These analytical formulas have been developed using full wave theory. We have discovered that the maxima of the mass sensitivity Sσvpf, Sσvph1 and maxima of the relative gradients (-(1/vp)dvp)⁄df, −(1/vp)dvp/dh1, occur virtually at the same values of fandh1. Comparing with the Perturbation Method and Finite Element Method (FEM), the analytical formulas established in this paper display some advantages, such as very low execution time of the mass sensitivity , and perhaps more importantly a possibility for a direct parametric optimization of the Love wave waveguide as a function of its material parameters, thickness of the guiding surface layer and wave frequency .