Dyadic Universal Functions and Simultaneous Near-Field/Far-Field Regularization of Elastodynamic Dyadic Green’s Functions for 3-D Mass-Loading Analysis in Microacoustic Devices

Assuming an infinite-domain isotropic elastic medium and a Dirac delta function vector-force excitation, fδ(x - x', y - y', z - z'), spectral domain dyadic Green's functions (DGFs) G for 3-D mass-loading analysis in microacoustic devices have been constructed. Thereby, equivalent inhomogeneous plane-wave (2-D Fourier transform) and homogeneous plane-wave (3-D Fourier transform) representations, G(k
₁
, k
₂
) and G(k
₁
, k
₂
, k
₃
), respectively, have been obtained in closed form. The construction of G(k
₁
, k
₂
) follows an earlier scheme by utilizing the diagonalization of the governing equations subject to the radiation condition. Consecutively, G(k
₁
, k
₂
) has been employed for obtaining the associated stress distributions. The latter distributions induce novel problem-tailored expressions for η-parameterized “smeared-out”Dirac delta functions δ
_η
(x - x', y - y'). Using δ
_η
(x - x', y - y'), exponentially regularized DGFs G
_η
(k
₁
, k
₂
) have been obtained. The notion of dyadic universal functions, also introduced earlier, has been utilized to demonstrate that the exponentially regularized DGFs can in addition be regularized algebraically. Finally, the operator inversion for the construction of ς(k
₁
, k
₂
, k
₃
) is carried out in closed form.