Sensitivity of Love surface waves to mass loading

The sensitivity of the phase velocity v(p) 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 sigma[kg/m(2)]. To this end, the we developed analytical formulas for the mass coefficient of sensitivity S-sigma(vp) = (1/v(p))dv(p)/d sigma [m(2)/kg] and phase velocity gradients -dv(p)(f)/df and -dv(p)(h(1))/dh(1), where f and h(1) 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 S-sigma(vp) with 1) the relative slope (gradient) -(1/v(p))dv(p)/dh(1) of the phase velocity dispersion curve vp(h(1)), and 2) the relative slope (gradient) -(1/v(p))dv(p)/df of the phase velocity dispersion curve v(p)(f). These analytical formulas have been developed using full wave theory. We have discovered that the maxima of the mass sensitivity S-sigma(vp) (f), S-sigma(vp) (h(1)) and maxima of the relative gradients (-(1/v(p))dv(p)) forward slash df, -(1/v(p))dv(p)/dh(1), occur virtually at the same values of f and h(1). 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 .