tianssss 发表于 2012-1-6 20:37:40

请教,这个矩阵如何求解特征值

syms lambda theta0 theta1 theta2 theta3
syms E1 E2 E3 nu1 nu2 nu3
mu1=E1/(2*(1+nu1))
mu2=E2/(2*(1+nu2))
mu3=E3/(2*(1+nu3))
kapa1=3-4*nu1
kapa2=3-4*nu2
kapa3=3-4*nu3
tao21=mu2/mu1
tao31=mu3/mu1
tao32=mu3/mu2
A=[lambda*exp(i*(lambda-1)*theta0),exp(-i*(lambda-1)*theta0),0,0,-lambda*exp(i*(lambda-1)*theta3),-exp(i*(lambda-1)*theta3),exp(i*(lambda+1)*theta0),0,0,0,-exp(i*(lambda+1)*theta3),0;
    exp(i*(lambda-1)*theta0),lambda*exp(-i*(lambda-1)*theta0),0,0,-exp(i*(lambda-1)*theta3),-lambda*exp(-i*(lambda-1)*theta3),0,exp(-i*(lambda+1)*theta0),0,0,0,-exp(-i*(lambda+1)*theta3);
    lambda*exp(i*(lambda-1)*theta1),exp(-i*(lambda-1)*theta1),-lambda*exp(i*(lambda-1)*theta1),-exp(-i*(lambda-1)*theta1),0,0,exp(i*(lambda+1)*theta1),0,-exp(i*(lambda+1)*theta1),0,0,0;
    exp(i*(lambda-1)*theta1),lambda*exp(-i*(lambda-1)*theta1),-exp(i*(lambda-1)*theta1),-lambda*exp(-i*(lambda-1)*theta1),0,0,0,exp(-i*(lambda+1)*theta1),0,-exp(-i*(lambda+1)*theta1),0,0;
    0,0,lambda*exp(i*(lambda-1)*theta2),exp(-i*(lambda-1)*theta2),-lambda*exp(i*(lambda-1)*theta2),-exp(i*(lambda-1)*theta2),0,0,exp(i*(lambda+1)*theta2),0,-exp(i*(lambda+1)*theta2),0;
    0,0,exp(i*(lambda-1)*theta2),lambda*exp(-i*(lambda-1)*theta2),-exp(i*(lambda-1)*theta2),-lambda*exp(-i*(lambda-1)*theta2),0,0,0,exp(-i*(lambda+1)*theta2),0,-exp(-i*(lambda+1)*theta2);
    tao31*kapa1*exp(i*(lambda-1)*theta0),-tao31*lambda*exp(-i*(lambda-1)*theta0),0,0,-kapa3*exp(i*(lambda-1)*theta3),lambda*exp(-i*(lambda-1)*theta3),0,-tao31*exp(-i*(lambda+1)*theta0),0,0,0,exp(-i*(lambda+1)*theta3);
    -tao31*lambda*exp(i*(lambda-1)*theta0),tao31*kapa1*exp(-i*(lambda-1)*theta0),0,0,lambda*exp(i*(lambda-1)*theta3),-kapa3*exp(-i*(lambda-1)*theta3),-tao31*exp(i*(lambda+1)*theta0),0,0,0,exp(i*(lambda+1)*theta3),0;
    tao21*kapa1*exp(i*(lambda-1)*theta1),-tao21*lambda*exp(-i*(lambda-1)*theta1),-kapa2*exp(i*(lambda-1)*theta1),lambda*exp(-i*(lambda-1)*theta1),0,0,0,-tao21*exp(-i*(lambda+1)*theta1),0,exp(-i*(lambda+1)*theta1),0,0;
    -lambda*tao21*exp(i*(lambda-1)*theta1),tao21*kapa1*exp(-i*(lambda-1)*theta1),lambda*exp(i*(lambda-1)*theta1),-kapa2*exp(-i*(lambda-1)*theta1),0,0,-tao21*exp(i*(lambda+1)*theta1),0,exp(i*(lambda+1)*theta1),0,0,0;
    0,0,tao32*kapa2*exp(i*(lambda-1)*theta2),-tao32*lambda*exp(-i*(lambda-1)*theta2),-kapa3*exp(i*(lambda-1)*theta2),lambda*exp(-i*(lambda-1)*theta2),0,0,0,-tao32*exp(-i*(lambda+1)*theta2),0,exp(-i*(lambda+1)*theta2);
    0,0,-tao32*lambda*exp(i*(lambda-1)*theta2),tao32*kapa2*exp(-i*(lambda-1)*theta2),lambda*exp(i*(lambda-1)*theta2),-kapa3*exp(-i*(lambda-1)*theta2),0,0,-tao32*exp(i*(lambda+1)*theta2),0,exp(i*(lambda+1)*theta2),0]

tianssss 发表于 2012-1-6 20:40:09

本帖最后由 tianssss 于 2012-1-6 20:46 编辑

矩阵A中,除了lambda外,其他的参数可以是一个数,假设A的行列式为零,如何把此时矩阵A的lambda值求出来?如果能画出在[-1,1]区间上det(A)的图来也行。

tianssss 发表于 2012-1-8 09:19:05

再顶一下,好心人帮帮忙。
页: [1]
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