Efficient spectral domain formulation of loading effects in acoustic sensors

The liquid loading effect on microacoustic sensors can be modeled using an acoustic impedance boundary condition. A rigorous expression for the acoustic impedance matrix in the spectral domain is derived for isotropic linear elastic layers backed by a defined impedance, which allows to model the loading effect resulting from non-uniform excitation. A wavenumber dependent matrix (3 × 3) is obtained, rather than the scalar shear and pressure impedances obtained by one-dimensional models (plane wave). This formulation is generalized to enclose linear viscous fluids. Furthermore, the impedance matrix is also calculated for problems with different boundary conditions such as half-space, free surface, rigid backing, and defined impedance boundary conditions. The latter enables the formulation to be applied to systems of layers of any number and composition. The results are compared to the 1D expressions of bulk impedance for the half-space and the transmission line equations for layers of finite thickness. In contrast to these 1D expressions, the coupling of pressure- and shear-wave propagation is considered which yields modified results. Furthermore, from the acoustic impedance matrices, Green's function matrices can be derived, which allow to model complex layered structure problems as will be outlined.