基于声压场描述的扩散声场多自由度互易原理研究

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

应用于复杂结构中频声振分析的扩散场多自由度互易原理采用位移变量描述系统,实质为弹性波场互易原理,应用于声波场时会造成模型自由度数不必要的增加。建立基于声压描述的扩散声场受挡模型,利用声辐射模态描述扩散声场中结构的表面受挡声压;据此提出基于声压描述的扩散声场多自由度互易原理,发现扩散声场中结构表面受挡声压的互谱矩阵与该结构在自由空间中振动辐射声波的声阻矩阵成正比。该互易原理与传统的单自由度互易原理表达形式相似,但适用于任意自由度结构。该互易原理可用于扩散声场中复杂结构的表面受挡声压的自谱及相关分析,仿真研究表明当边界元网格尺寸小于声波波长的1/6(线性单元)或1/3(二次单元)时,数值解与理论解完全吻合。

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.