Abstract: Sound absorption performance of porous materials is closely related to materials properties, size and shape of the hole and pore-distribution mode. It is significant to research and design porous materials for high sound-absorbing performance. In this paper, the relations between sound energy absorption rate and size and porosity of the materials were presented by studying sound propagation characteristics of porous metallic materials and structures based on surface impedance method and transfer matrix method. Then, an optimization problem was proposed and solved. In the optimization, sound energy absorption rate of the porous structure under a specific frequency was taken as an objective function, and the change rule of the size of cylindrical holes across material thickness was taken as the design parameter. Finally, a gradient porous structure with higher sound energy absorption rate was given through the optimizing design.

Key words: vibration and wave, metal porous materials, sound absorption, design optimization, surface impedance, transfer matrix method

摘要： 多孔材料的吸声性能依赖于基体材料的性质、孔的形状与尺寸以及孔隙分布方式。利用多孔材料的高吸声性能和可设计性特点，研究和设计高吸声制材料与结构意义重大。采用表面阻抗法和传递矩阵法研究规则有序的圆柱形孔多孔金属材料与结构的声传播特性，建立声能吸收率与孔的尺寸和孔隙率之间的解析关系，并以圆柱形孔的尺寸沿材料厚度方向的变化规律为设计参数，建立以特定频率下层状多孔结构声能吸收率为目标的优化问题的提法和求解方法，得到一种具有较高声能吸收率的梯度多孔结构。

关键词: 振动与波, 金属多孔材料, 吸声, 优化设计, 表面阻抗, 传递矩阵