The research about the multi-freedom degree reciprocity principle for diffuse sound field based on the sound pressure field description

The multi-freedom degree reciprocity principle for diffuse field was proposed and applied in mid-frequency analysis of complex vibro-acoustic system recently. In nature, this reciprocity principle should be an elastic wave field reciprocity principle, since the vibro-acoustic system is described by displacement variables. The application of this diffuse reciprocity principle in the sound wave field will lead the model to be unnecessarily too complex. One multi-freedom degree acoustic reciprocity principle more applicable for diffuse sound field is proposed here. Firstly, the "blocked" model of diffuse sound field is proposed to describe the blocked sound pressure on the surface of a structure excited by the diffuse sound field via sound radiation modes. Secondly, the multi-freedom degree reciprocity principle for the diffuse sound field based on the sound pressure description is proposed, which shows that the cross-spectrum matrix of the blocked sound pressure on the surface of a structure in the diffuse sound field is directly proportional to the real part of acoustic impedance matrix of free-space sound radiation. This reciprocity principle is shown to be similar form with the traditional single-freedom degree one, but applicable for the structure with arbitrary degrees of freedom. This reciprocity principle can be applied in the auto-spectrum and correlation analysis of blocked sound pressure on the surface of arbitrary shaped structure in diffuse sound field. The numerical simulations show that the numerical results are consistent with the theoretical ones provided that the mesh size of boundary elements is smaller than one-sixth (linear element) or one-third (quadratic element) of acoustic wavelength.