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 σ kg / m 2 . To this end, the we developed analytical formulas for the mass coefficient of sensitivity S σ v p = ( 1 / v p ) d v p / d σ [ m 2 / kg ] and phase velocity gradients − d v p ( f ) / d f and − d v p ( h 1 ) / d h 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 σ v p with 1) the relative slope (gradient) − ( 1 / v p ) d v p / d h 1 of the phase velocity dispersion curve v p ( h 1 ) , and 2) the relative slope (gradient) − ( 1 / v p ) d v p / d f 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 σ v p f , S σ v p h 1 and maxima of the relative gradients ( - ( 1 / v p ) d v p ) ⁄ d f , − ( 1 / v p ) d v p / d h 1 , occur virtually at the same values of f a nd 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 . • Exact analytical model of Love wave sensors based on first principles was developed. • Exact analytical formulas for mass sensitivity of Love wave sensors were developed. • New formulas can significantly accelerate the design process of Love wave sensors. • Mass sensitivity is proportional to gradient of the phase velocity dispersion curves.