含未知数的矩阵行列式为0 如何求解未知数。

代码如下

clear

L=50;

H=1;

b=0.5;

E=210E6;

rou=7860;

delta=0;

I=b*H^3/12;

A=b*H;

h=0;

s=25;

C=2*H/E/I*(delta/(1-delta)^2)*(5.93-19.69*delta+37.14*delta^2-35.84*delta^3+13.12*delta^4);

syms w

a=(w^2*rou*A/E/I)^(1/4);

K=[0 1 0 1 0 0 0 0;

0 -1 0 -1 0 0 0 0;

0 0 0 0 sin(a*L) cos(a*L) h*sin(a*L) h*cos(a*L);

0 0 0 0 -sin(a*L) -cos(a*L) -h*sin(a*L) -h*cos(a*L);

sin(a*s) cos(a*s) h*sin(a*s) h*cos(a*s) -sin(a*s) -cos(a*s) -h*sin(a*s) -h*cos(a*s);

cos(a*s) -sin(a*s) h*cos(a*s) h*sin(a*s) -cos(a*s)+C*E*I*a*sin(a*s) sin(a*s)+C*E*I*a*cos(a*s) -h*cos(a*s)+C*E*I*a*h*sin(a*s) h*sin(a*s)+C*E*I*a*h*cos(a*s);

-sin(a*s) -cos(a*s) -h*sin(a*s) -h*cos(a*s) sin(a*s) cos(a*s) h*sin(a*s) h*cos(a*s);

-cos(a*s) sin(a*s) -h*cos(a*s) h*sin(a*s) cos(a*s) -sin(a*s) h*cos(a*s) -h*sin(a*s)];

vpa(solve(det(K)==0))

发生错误

错误使用 sym/solve (line 266)

Specify the variable to solve for.

出错 ceshi (line 45)

vpa(solve(det(K)==0))

Answer 1

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clear

L=50;

H=1;

b=0.5;

E=210E6;

rou=7860;

delta=0;

I=b*H^3/12;

A=b*H;

h=0;

s=25;

C=2*H/E/I*(delta/(1-delta)^2)*(5.93-19.69*delta+37.14*delta^2-35.84*delta^3+13.12*delta^4);

syms w

a=(w^2*rou*A/E/I)^(1/4);

K=[0 1 0 1 0 0 0 0;

0 -1 0 -1 0 0 0 0;

0 0 0 0 sin(a*L) cos(a*L) h*sin(a*L) h*cos(a*L);

0 0 0 0 -sin(a*L) -cos(a*L) -h*sin(a*L) -h*cos(a*L);

sin(a*s) cos(a*s) h*sin(a*s) h*cos(a*s) -sin(a*s) -cos(a*s) -h*sin(a*s) -h*cos(a*s);

cos(a*s) -sin(a*s) h*cos(a*s) h*sin(a*s) -cos(a*s)+C*E*I*a*sin(a*s) sin(a*s)+C*E*I*a*cos(a*s) -h*cos(a*s)+C*E*I*a*h*sin(a*s) h*sin(a*s)+C*E*I*a*h*cos(a*s);

-sin(a*s) -cos(a*s) -h*sin(a*s) -h*cos(a*s) sin(a*s) cos(a*s) h*sin(a*s) h*cos(a*s);

-cos(a*s) sin(a*s) -h*cos(a*s) h*sin(a*s) cos(a*s) -sin(a*s) h*cos(a*s) -h*sin(a*s)];

vpa(solve(det(K)==0,w))