Mass sensitivity analysis for planar acoustic sensors by the perturbation method

Mass sensitivity formulae of the acoustic gravimetric sensors of the two lowest sagittal modes and the shear horizontal (SH) modes in a two-layer composite are derived by using the perturbation method. The composite consists of a solid isotropic plate of thickness of b coated by one solid isotropic film of thickness h. The coating layer is assumed to be acoustically thin (h≪/λ), where λ is the acoustic wavelength. The mass sensitivity formulae include the elastic and geometric parameters of the two-layer composite and the mass loading layer. The formulae reduce to those found by solving the boundary value problem of a multilayer composite for the lowest extensional (sagittal) mode and for the SH modes by taking the mass loading layer material to be the same material as the coating layer. The results obtained by the two methods are not consistent for the lowest flexural plate mode and an explanation for this is provided