WAN Quan  ZHANG Haibin  JIANG Weikang

(State Key Laboratory of Mechanical System and Vibration, Shanghai Jiaotong University  Shanghai  200240)

Received Jan. 13, 2009

Revised Feb. 20, 2009

Abstract The multi-DOF (degree-of-freedom) reciprocity principle for diffuse field was proposed and applied in the mid-frequency analysis of a complex vibro-acoustic system. As the application of this diffuse reciprocity principle in a sound field leads the model to be necessarily enormous, one multi-DOF acoustic reciprocity principle more applicable for diffuse sound field is proposed here. First, the “blocked” model of diffuse sound field is proposed to describe the blocked sound pressure on the surface of a structure excited by a diffuse sound field via sound radiation modes. Then, the multi-DOF reciprocity principle for 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 a diffuse sound field is directly proportional to the real part of the acoustic impedance matrix of free field sound radiation. It shows that the reciprocity principle is the similar form with the traditional single-DOF one, but applicable for the structure with arbitrary degrees of freedom. And show that this reciprocity principle can be applied in the auto-spectrum and the correlation analysis of the blocked sound pressure on the surface of an arbitrary shaped structure in a diffuse sound field. Numerical simulations show that the numerical results are consistent with the theoretical ones provide that the mesh size of boundary elements is smaller than one-sixth (linear element) or one-third (quadratic element) of the acoustic wavelength.

PACS numbers: 43.20, 43.28, 43.40