1.声学超材料的特征为：亚波长条件下的周期性布置振子

2.具体计算公式如下：

Matlab实现

function [F,TL] = MetamaterialPlate(rho,E,h,v,phi,lbx,lby,gamma,nr,fr)%输入板的密度、杨氏模量、板厚、泊松比、声波入射角、胞元尺寸、振子质量比、振子阻尼、振子共振频率
j = 1i;
F=zeros(10000,1);
TL=zeros(10000,1);
%% 空气参数定义
    rho0 = 1.2;         %空气密度
    c0 = 340;           %空气声速
%% 平板参数定义
    D = E*h^3/(12*(1-v^2)); %板的弯曲刚度
    m = rho*h*lbx*lby;      %单个胞元面积内板的质量
%% 振子定义  
    mr = gamma*m;           %振子质量
    wr = 2*pi*fr;           %振子共振角频率
%% 隔声系数计算
for f = 1:1:100000
    w = 2*pi*f;
    k0 = w/c0;
    meq = mr/(1-w^2/(wr^2*(1+j*nr)));       %等效动态质量
    rhoeff = (m+meq)/(lbx*lby*h);           %等效动态质量密度
    delta = D*(k0*sin(phi))^4-rhoeff*h*w^2+2*1i*rho0*c0*w/cos(phi);
    t = (2*rho0*c0*w/(delta*cos(phi)))^2;
    F(f) = f;    
    TL(f) = 10*log10(1/t);
end
semilogx(F,TL,'k','linewidth',2);
end

 3.参数定义如下

MetamaterialPlate(2700,70e9,0.005,0.33,pi/6,0.035,0.035,0.2,0.005,300);

4.结果对比

 5.参考文献