1.Laboratory of Science and Technology on Integrated Logistics Support, College of Intelligence Science and Technology, National University of Defense Science and technology, Changsha 410073, China 2.College of Engineering and Technology, Southwest university, Chongqing 400715, China
Abstract:In this paper, we propose a hybrid subwavelength broadband sound absorber based on micro perforated plate and multiple coiled channels. And the mechanism of low frequency broadband sound absorption of the hybrid sound absorber is analyzed in detail. Based on this, the theoretical analysis model and the finite element numerical analysis model are established, and the mutual verification of theoretical and numerical solutions is completed. The structure can theoretically achieve the low-frequency and high-efficiency sound absorption with an average absorption coefficient of 0.8 in a frequency band of 200–500 Hz when the overall thickness of the sound absorbing structure is 60 mm. At the same time when the overall thickness is 90 mm, quasi-perfect sound absorption with peaks up to 0.95 in a frequency range of 180–350 Hz is realized theoretically. The composite sound absorption structure has a certain application prospect in engineering low frequency noise in future. Keywords:micro-perforated plate/ coiled channels/ hybrid sound absorber/ low frequency sound absorption
2.复合吸声结构的吸声理论分析减小吸声结构厚度的有效方法是引入空间盘绕或迷宫式结构[18]. 本文设计并验证了一种由微穿孔板(穿孔直径小于1 mm)和折曲FP通道组合而成的复合声学超材料. 该结构在传统微穿孔板的基础上, 将背腔进行折曲处理, 使其可以不增加总厚度而大大增强对低频噪声的吸收性能. 同时, 将共振频率不同的吸声单元结构并联设计, 使其能在不添加其他吸收性材料(吸声棉等)[19,20]的情况下获得较宽的吸收带宽. 如图1所示, 该复合吸声结构由微穿孔板和折曲FP通道组成, 入射声波沿Z轴进入垂直于微穿孔板的通道. 为探究其吸声机理, 本文首先建立一个如图1(d)所示的5通道单元的二维模型, 声波在盘绕通道内的传播路径如蓝色虚线箭头所示. 其中, 微穿孔板的主要结构参数有孔径$d$、板厚$t$和穿孔率$p$, 周期性通道的主要结构参数包括长度$L$、宽度$W$和高度$H$, 等效吸声长度$D$, 内部隔板厚度$t$. 在理论分析中, 折曲FP通道可简化为串联的多个直同轴连接子通道, 各子通道内的有效传播长度表示为${L_{{\rm{eff}}i}}\left( {i = 1, 2, 3,\cdots} \right)$. 图 1 复合声学超材料的结构及理论模型 (a) 微穿孔板; (b) 折曲通道; (c)吸声结构三维模型; (d) 吸声结构二维理论模型 Figure1. Structure and theoretical model of composite acoustic metamaterial: (a) The top micro-perforated panel (thickness $t$, diameter $d$, perforation rate $p$); (b) multiple coiled FP channels; (c) schematic of the hybrid metamaterial absorber composed of a microperforated panel (MPP) as a top face sheet and coiled-up Fabry–Perot (FP) channels with folding number n; (d) an approximate analytical two dimensional (2 D) model of one unit cell of a space-coiled metamaterial. All the widths of the channels in the YZ plane are $L$. The height of the channel along the Z axis is $H$.
3.低频宽带吸声机理分析为了对复合吸声结构的低频宽带吸声机理进行研究, 本文进一步使用COMSOL Multiphsics 5.3内嵌的声-热黏性声学耦合模块建立了该复合吸声结构的有限元分析数值模型, 假设该复合吸声结构所有内壁都为硬声学边界. 建立如图1(c)所示的由微穿孔板和多个盘绕通道组成的复合声学吸声结构的有限元分析模型并进行数值计算. 为探究其低频吸声机理, 在图2(a)中绘制了频率为230 Hz的声波传入吸声器时通道内部的声粒子速度(红色箭头)分布情况. 在微穿孔板与第一通道入口处观察到较大的粒子速度, 可以判断出, 由于微孔处粒子振动速度较大, 入射波能量主要是由声波与小孔之间的较大摩擦而耗散的. 图2(b)中绘制了230 Hz声波传入吸声器时通道内部的多切面声压分布图, 可以观察到, 此时黑色虚线内的两个通道折叠数为5的吸声单元对声波的耗散作用最为明显, 即折叠通道数多的单元(等效吸声长度大)对低频声波起主要吸声作用, 而折叠通道数少的单元(等效吸声长度小)对相对高频声波起主要吸声作用. 图 2 230 Hz声波传入时吸声器内声速与声压 (a)声速分布(m/s); (b)声压分布(Pa) Figure2. Sound velocity and sound pressure in a sound absorber when a 230 Hz sound wave is introduced: (a) Sound velocity distribution (m/s); (b) sound pressure distribution (Pa). The absorbers are constructed using the coiled-up channel with geometric parameters: $H = {\rm{59\;mm}}$, ${L_1} = {L_2} = {L_3} = {L_4} = {L_5} = 4.8{\rm{5\;mm}}$ and $W = 13.6\;{\rm{ mm}}$ and $d = {t_0} = {t_1} = 1\;{\rm{ mm}}$.
为了进一步研究所设计的复合吸声结构的吸声机理, 使用图形法研究了该复合吸声结构在复频率表面内的反射系数$\gamma $的分布[18]. 一般地, 在无损情况下, 反射系数包含共轭零点和极点, 如果在某一频率下达到完美吸声, 则零点将恰好位于实轴上. 图3(a)中绘制了该复合吸声结构在复频率表面内的$\lg | r |^2$的分布情况, 可以看出, 200—250 Hz范围内的零点都落在实轴附近, 因此, 在共振频率下可获得近乎完美吸收. 而高于250 Hz的零点偏移实轴较远, 并没有达到完美吸声. 零点和极点之间的距离也可以表征吸声带宽, 随着共振频率的降低, 零点和极点之间的距离逐渐减小的同时吸声带宽逐渐变窄. 图 3 复合吸声结构的吸声特性 (a) 反射系数零、极点分布; (b)吸声性能曲线; (c)声阻抗的实部与虚部 Figure3. Sound absorption characteristics of composite sound absorption structure: (a) Zero and pole distributions of reflection coefficients on complex frequency plane; (b) sound absorption performance curve. The dotted line is the theoretical solution and the solid line is the numerical solution, the black dotted line is the theoretical solution of each unit (Gradually increase the equivalent sound absorption length from left to right); (c) real and imaginary parts of relative impedance.
表1准完美吸声结构各吸声单元结构参数 Table1.Structural parameters of each sound absorption unit of quasi-perfect sound absorption structure.
图 4 复合吸声结构的准完美吸声特性 (a) 反射系数零、极点分布; (b)吸声性能曲线; (c)声阻抗的实部与虚部 Figure4. Quasi-perfect sound absorption characteristics of composite sound absorption structure: (a) Zero and pole distributions of reflection coefficients on complex frequency plane; (b) sound absorption performance curve, The dotted line is the theoretical solution and the solid line is the numerical solution; (c) real and imaginary parts of relative impedance.
图 1 复合声学超材料的结构及理论模型 (a) 微穿孔板; (b) 折曲通道; (c)吸声结构三维模型; (d) 吸声结构二维理论模型
图 2 230 Hz声波传入时吸声器内声速与声压 (a)声速分布(m/s); (b)声压分布(Pa)
图 3 复合吸声结构的吸声特性 (a) 反射系数零、极点分布; (b)吸声性能曲线; (c)声阻抗的实部与虚部
图 4 复合吸声结构的准完美吸声特性 (a) 反射系数零、极点分布; (b)吸声性能曲线; (c)声阻抗的实部与虚部