The disturbance of a plane dyadic wave by a small spherical cavity

Dyadic scattering offers a general setting for solving wave-obstacle interaction problems in Continuum Mechanics, because it eliminates the direction of polarization from the scattering formulation. Once the dyadic problem has been solved, any classical scattering problem for the displacement field is recoverable through a contraction with the given polarization. In the present work we solve the scattering problem of a plane dyadic incident field which is disturbed by a spherical cavity in the medium of propagation. The cavity is considered to be small in the sense that its characteristic dimension is much less than the wave length of the incident field. The zeroth and the first order low-frequency approximations of the near field as well as the leading approximation of the far-field (which is of the third order) are obtained explicitly via an appropriate generalization of the Papkovich representation for dyadic fields. The leading approximation of the scattering cross-section is also provided. The results are then used to check the credibility of related vector results obtained from the Boundary Element Method and an amazing coincidence is observed, at least for small enough frequencies.