Analytical solutions for sagittal plane waves in three-layer composites

The analytic dispersion equations for the symmetric and antisymmetric saggital plane plate modes of a three-layer composite system are presented. The composite consists of a solid isotropic plate sandwiched between two acoustically thin (<0.02 lambda) isotopic solid layers, where lambda is the acoustic wavelength. The thin layers are considered either as the mass loading or the chemical selective coating layers for the plate wave sensors. Explicit formulas which identify the contributions of the elasticity and inertia effects for the phase velocity and mass loading sensitivity of the lowest symmetric (S(0)) and antisymmetric (A(0)) mode for the case where the thickness of the composite plate is much less than lambda are obtained. The amounts by which the elasticity of the thin layer and the inertia decrease the mass loading sensitivity is found for both sensors. It is also found that the sensitivity of the A(0) mode significantly depends on the operating frequency but that of the S(0) mode does not. Specific examples are given for the case of a fused silica plate sandwiched by two thin lucite layers.