In this paper, the gradient anechoic coating whose density changes exponentially along direction of thickness is investigated. A numerical model is established by finite element method (FEM) to analyze the underwater sound absorption performance under different density distribution. The calculation results show that the exponential anechoic coating has better sound absorption performance compared with the homogeneous medium and linear anechoic coating. In addition, a discrete layered method is proposed to achieve gradient characteristics. In order to change the equivalent density of each layer, periodically distributed semi-cylindrical steel scatterers with different diameters are embedded in each layer. Therefore, the density function of the whole coating changes in exponential gradient with stepped function. Based on the sound absorption mechanism of multiple scattering and waveform conversion, the sound absorption is improved in low-frequency band from 0 Hz to 1000 Hz. The exponential gradient anechoic coating has potential applications in underwater sound absorption and vibration control.

本文研究了密度沿厚度方向呈指数变化的梯度消声涂层。采用有限元法（FEM）建立数值模型，分析不同密度分布下的水下吸声性能。计算结果表明，指数消声涂层与均质介质和线性消声涂层相比具有更好的吸声性能。此外，提出了一种离散分层方法来实现梯度特性。为了改变每一层的等效密度，在每一层中嵌入了周期性分布的不同直径的半圆柱形钢质散射体。因此，整个涂层的密度函数呈指数梯度变化，呈阶梯函数。基于多重散射和波形转换的吸声机理，在0Hz到1000Hz的低频段提高了吸声效果。指数梯度消声涂层在水下吸声和振动控制方面具有潜在应用。