A model of the acoustic impedance matrix was proposed to describe the local and non-local properties of acoustic scattering. The derivation of an acoustic impedance matrix and its algebraic model were completed. On the basis of the viscoelastic finite element method a numerical calculation code was programmed. The code validation and its calculation precision were proven. Finally, an acoustic impedance matrix was computed for a viscoelastic plate backed by a rigid body, and its parameters from an algebraic model were fitted. The local and non-local properties of acoustic impedance and the variation of parameters in the model were analyzed in detail. The results of the experiment show that the non-local properties of viscoelastic material surface acoustic scattering impedance can be described, both qualitatively and quantitatively by the acoustic impedance matrix and non-local acoustic impedance algebraic model. Therefore, an effective numerical calculation method was proposed to research the non-local properties of acoustic impedance.%针对刚性背衬下的粘弹性材料层,提出了一种能够描述表面声散射的局域/非局域特性的声阻抗矩阵模型,进行了声阻抗矩阵及代数模型的推导.以粘弹性有限元为基础完成了数值计算工具的开发,并对自编代码进行了校核,表明数值工具具有较高的计算精度.计算了刚性背衬下粘弹性板的声阻抗矩阵,并拟合得到声阻抗模型参数,分析了声阻抗局域、非局域特性及代数模型中各参数的变化规律.实际计算结果表明:声阻抗矩阵和非局域声阻抗代数模型能够定性和定量描述粘弹性材料表面声散射阻抗的非局域特性,为声阻抗非局域特性的研究提供了一个有效的数值分析方法.
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