zs2.m

基于瑞利波及lamb波的频散曲线程序,可用于根据实验绘制Rali波及lamb波的频散曲线,检验其在不同材料中的频散特性

%求解Lame波对称部分的模态S2/S3
format long
syms c;   %定义速度c为符号函数
kh=4.5;      %k为波数，h为总的板厚
cd=5790;cs=3200; %cd为纵波波速，cs为横波波速
y1=-4*tan(kh/2*((c/cd)^2-1)^(1/2))*((c/cd)^2-1)^(1/2)*((c/cs)^2-1)^(1/2);
y2=(2-(c/cs)^2)^2*tan(kh/2*((c/cs)^2-1)^(1/2));
c=[7400;7450];
eps=1e-12;
xx=[];
for i=2:2
    a=c(i-1);b=c(i);
    c=(a+b)/2;
    while (subs(y1-y2)~= 0) & ((b-a)>eps)
        c=(a+b)/2;
        fa=-4*tan(kh/2*((a/cd)^2-1)^(1/2))*((a/cd)^2-1)^(1/2)*((a/cs)^2-1)^(1/2)-(2-(a/cs)^2)^2*tan(kh/2*((a/cs)^2-1)^(1/2));
        fb=-4*tan(kh/2*((b/cd)^2-1)^(1/2))*((b/cd)^2-1)^(1/2)*((b/cs)^2-1)^(1/2)-(2-(b/cs)^2)^2*tan(kh/2*((b/cs)^2-1)^(1/2));
        fy=-4*tan(kh/2*((c/cd)^2-1)^(1/2))*((c/cd)^2-1)^(1/2)*((c/cs)^2-1)^(1/2)-(2-(c/cs)^2)^2*tan(kh/2*((c/cs)^2-1)^(1/2));
        if fa*fy < 0
            b=c;
        else
            a=c;
        end
    end
    xx=[xx;c]
    m=subs(y1-y2)
end