Reciprocity relationship for the diffuse reverberant loading on a general structure

Abstract

Diffuse field reciprocity relates the diffuse reverberant loading on a structure to its radiation impedance. Such a relationship has been previously derived for the ensemble average response of the structure in connection to structural or acoustical subsystems with uncertain boundaries. In the present work, a different reciprocity relationship is derived from the direct boundary integral formulation for the scattering problem, in which the diffuse reverberant loading on the structure depends on both the radiation impedance and the free field Green's function. It is revealed that the difference in the reciprocity relationships results from the different definitions of the diffuse fields. Diffuse reverberant loading is analytically investigated for two examples. Possible extension of the present reciprocity relationship to a structural system is also discussed. It is shown that the reciprocity relationships are equivalent when the definitions of the diffuse fields are identical or the curvature radius of the structure is much larger than the wavelength involved.