fsolve求解12​阶行列式方程（超越方​程），遇到错误。

E2=76e9;

rho2=10500;

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E1=160e9;

rho1=2300;

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h1=2*1e-6;

h2=5*1e-6;

h0=h2-h1;

a=150*1e-6;

b=350*1e-6;

l=500*1e-6;

z=10*1e-6;

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co=1; %缩小系数

syms omiga;

beta1=(10.15179*(co*omiga)^0.5) %beta1、2、3分别为以下行列式中的参数

beta2=(10.1533*(co*omiga)^0.5)

beta3=(10.15179*(co*omiga)^0.5)

for i=1:2000 %求解超越方程特征根，以下12阶行列式中omiga为待求解的未知数

root(i)=fsolve(@(omiga) det([0,1,0,1,0,0,0,0,0,0,0,0;

beta1,0,beta1,0,0,0,0,0,0,0,0,0;

0,0,0,0,0,0,0,0,sin(beta3*l),cos(beta3*l),sinh(beta3*l),cosh(beta3*l);

0,0,0,0,0,0,0,0,beta3*cos(beta3*l),-beta3*sin(beta3*l),beta3*cosh(beta3*l),beta3*sinh(beta3*l);

sin(beta1*a),cos(beta1*a),sinh(beta1*a),cosh(beta1*a),-sin(beta2*a),-cos(beta2*a),-sinh(beta2*a),-cosh(beta2*a),0,0,0,0;

0,0,0,0,sin(beta2*b),cos(beta2*b),sinh(beta2*b),cosh(beta2*b),-sin(beta3*b),-cos(beta3*b),-sinh(beta3*b),-cosh(beta3*b);

beta1*cos(beta1*a),-beta1*sin(beta1*a),beta1*cosh(beta1*a),beta1*sinh(beta1*a),-beta2*cos(beta2*a),beta2*sin(beta2*a),-beta2*cosh(beta2*a),-beta2*sinh(beta2*a),0,0,0,0;

0,0,0,0,beta2*cos(beta2*b),-beta2*sin(beta2*b),beta2*cosh(beta2*b),beta2*sinh(beta2*b),-beta3*cos(beta3*b),beta3*sin(beta3*b),-beta3*cosh(beta3*b),-beta3*sinh(beta3*b);

-((2*z/3)*(E1*(h1)^3+E2*((h2)^3-(h1)^3)))*((beta1)^2)*sin(beta1*a),-((2*z/3)*(E1*(h1)^3+E2*((h2)^3-(h1)^3)))*((beta1)^2)*cos(beta1*a),((2*z/3)*(E1*(h1)^3+E2*((h2)^3-(h1)^3)))*((beta1)^2)*sinh(beta1*a),((2*z/3)*(E1*(h1)^3+E2*((h2)^3-(h1)^3)))*((beta1)^2)*cosh(beta1*a),(2*E2*z*((h2^3-h1^3)/3))*((beta2)^2)*sin(beta2*a),(2*E2*z*((h2^3-h1^3)/3))*((beta2)^2)*cos(beta2*a),-(2*E2*z*((h2^3-h1^3)/3))*((beta2)^2)*sinh(beta2*a),-(2*E2*z*((h2^3-h1^3)/3))*((beta2)^2)*cosh(beta2*a),0,0,0,0;

0,0,0,0,-(2*E2*z*((h2^3-h1^3)/3))*((beta2)^2)*sin(beta2*b),-(2*E2*z*((h2^3-h1^3)/3))*((beta2)^2)*cos(beta2*b),(2*E2*z*((h2^3-h1^3)/3))*((beta2)^2)*sinh(beta2*b),(2*E2*z*((h2^3-h1^3)/3))*((beta2)^2)*cosh(beta2*b),((2*z/3)*(E1*(h1)^3+E2*((h2)^3-(h1)^3)))*((beta3)^2)*sin(beta3*b),((2*z/3)*(E1*(h1)^3+E2*((h2)^3-(h1)^3)))*((beta3)^2)*cos(beta3*b),-((2*z/3)*(E1*(h1)^3+E2*((h2)^3-(h1)^3)))*((beta3)^2)*sinh(beta3*b),-((2*z/3)*(E1*(h1)^3+E2*((h2)^3-(h1)^3)))*((beta3)^2)*cosh(beta3*b);

-((2*z/3)*(E1*(h1)^3+E2*((h2)^3-(h1)^3)))*((beta1)^3)*cos(beta1*a),((2*z/3)*(E1*(h1)^3+E2*((h2)^3-(h1)^3)))*((beta1)^3)*sin(beta1*a),((2*z/3)*(E1*(h1)^3+E2*((h2)^3-(h1)^3)))*((beta1)^3)*cosh(beta1*a),((2*z/3)*(E1*(h1)^3+E2*((h2)^3-(h1)^3)))*((beta1)^3)*sinh(beta1*a),(2*E2*z*((h2^3-h1^3)/3))*((beta2)^3)*cos(beta2*a),-(2*E2*z*((h2^3-h1^3)/3))*((beta2)^3)*sin(beta2*a),-(2*E2*z*((h2^3-h1^3)/3))*((beta2)^3)*cosh(beta2*a),-(2*E2*z*((h2^3-h1^3)/3))*((beta2)^3)*sinh(beta2*a),0,0,0,0;

0,0,0,0,-(2*E2*z*((h2^3-h1^3)/3))*((beta2)^3)*cos(beta2*b),(2*E2*z*((h2^3-h1^3)/3))*((beta2)^3)*sin(beta2*b),(2*E2*z*((h2^3-h1^3)/3))*((beta2)^3)*cosh(beta2*b),(2*E2*z*((h2^3-h1^3)/3))*((beta2)^3)*sinh(beta2*b),((2*z/3)*(E1*(h1)^3+E2*((h2)^3-(h1)^3)))*((beta3)^3)*cos(beta3*b),-((2*z/3)*(E1*(h1)^3+E2*((h2)^3-(h1)^3)))*((beta3)^3)*sin(beta3*b),-((2*z/3)*(E1*(h1)^3+E2*((h2)^3-(h1)^3)))*((beta3)^3)*cosh(beta3*b),-((2*z/3)*(E1*(h1)^3+E2*((h2)^3-(h1)^3)))*((beta3)^3)*sinh(beta3*b)]),i,optimset('display','off'));

end

ro1=root;

j_tem=1;

k_tem=1;

for i_tem=1:1999 %去重根

b_tem(i_tem)=ro1(i_tem+1);

end

b_tem(2000)=ro1(2000);

c_tem=b_tem-ro1;

c_tem_find_first= find( c_tem>0.1);

r_tem(j_tem)=ro1(c_tem_find_first(1));

r_tem(j_tem+1)=b_tem(c_tem_find_first(1));

j_tem=j_tem+2;

for i_c=c_tem_find_first(2):2000

if c_tem(i_c)>0.1

r_tem(j_tem)=b_tem(i_c);

j_tem=j_tem+1;

end

end

r_tem;

for i_re=1:j_tem-2

root_return(i_re)=r_tem(i_re+1);

end

root_return;

ri=root_return/co

Answer 1

[xuwfuum]

仅供参考

E2=76e9;
rho2=10500;
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E1=160e9;
rho1=2300;
%%%%
h1=2*1e-6;
h2=5*1e-6;
h0=h2-h1;
a=150*1e-6;
b=350*1e-6;
l=500*1e-6;
z=10*1e-6;


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co=1;                      %缩小系数
beta1=@(omiga)(10.15179*(co*omiga)^0.5);                       %beta1、2、3分别为以下行列式中的参数
beta2=@(omiga)(10.1533*(co*omiga)^0.5);
beta3=@(omiga)(10.15179*(co*omiga)^0.5);
for i=1:2000                 %求解超越方程特征根，以下12阶行列式中omiga为待求解的未知数
    root(i)=fsolve(@(omiga) det([0,1,0,1,0,0,0,0,0,0,0,0;
        beta1(omiga),0,beta1(omiga),0,0,0,0,0,0,0,0,0;
        0,0,0,0,0,0,0,0,sin(beta3(omiga)*l),cos(beta3(omiga)*l),sinh(beta3(omiga)*l),cosh(beta3(omiga)*l);
        0,0,0,0,0,0,0,0,beta3(omiga)*cos(beta3(omiga)*l),-beta3(omiga)*sin(beta3(omiga)*l),beta3(omiga)*cosh(beta3(omiga)*l),beta3(omiga)*sinh(beta3(omiga)*l);
        sin(beta1(omiga)*a),cos(beta1(omiga)*a),sinh(beta1(omiga)*a),cosh(beta1(omiga)*a),-sin(beta2(omiga)*a),-cos(beta2(omiga)*a),-sinh(beta2(omiga)*a),-cosh(beta2(omiga)*a),0,0,0,0;
        0,0,0,0,sin(beta2(omiga)*b),cos(beta2(omiga)*b),sinh(beta2(omiga)*b),cosh(beta2(omiga)*b),-sin(beta3(omiga)*b),-cos(beta3(omiga)*b),-sinh(beta3(omiga)*b),-cosh(beta3(omiga)*b);
        beta1(omiga)*cos(beta1(omiga)*a),-beta1(omiga)*sin(beta1(omiga)*a),beta1(omiga)*cosh(beta1(omiga)*a),beta1(omiga)*sinh(beta1(omiga)*a),-beta2(omiga)*cos(beta2(omiga)*a),beta2(omiga)*sin(beta2(omiga)*a),-beta2(omiga)*cosh(beta2(omiga)*a),-beta2(omiga)*sinh(beta2(omiga)*a),0,0,0,0;
        0,0,0,0,beta2(omiga)*cos(beta2(omiga)*b),-beta2(omiga)*sin(beta2(omiga)*b),beta2(omiga)*cosh(beta2(omiga)*b),beta2(omiga)*sinh(beta2(omiga)*b),-beta3(omiga)*cos(beta3(omiga)*b),beta3(omiga)*sin(beta3(omiga)*b),-beta3(omiga)*cosh(beta3(omiga)*b),-beta3(omiga)*sinh(beta3(omiga)*b);
        -((2*z/3)*(E1*(h1)^3+E2*((h2)^3-(h1)^3)))*((beta1(omiga))^2)*sin(beta1(omiga)*a),-((2*z/3)*(E1*(h1)^3+E2*((h2)^3-(h1)^3)))*((beta1(omiga))^2)*cos(beta1(omiga)*a),((2*z/3)*(E1*(h1)^3+E2*((h2)^3-(h1)^3)))*((beta1(omiga))^2)*sinh(beta1(omiga)*a),((2*z/3)*(E1*(h1)^3+E2*((h2)^3-(h1)^3)))*((beta1(omiga))^2)*cosh(beta1(omiga)*a),(2*E2*z*((h2^3-h1^3)/3))*((beta2(omiga))^2)*sin(beta2(omiga)*a),(2*E2*z*((h2^3-h1^3)/3))*((beta2(omiga))^2)*cos(beta2(omiga)*a),-(2*E2*z*((h2^3-h1^3)/3))*((beta2(omiga))^2)*sinh(beta2(omiga)*a),-(2*E2*z*((h2^3-h1^3)/3))*((beta2(omiga))^2)*cosh(beta2(omiga)*a),0,0,0,0;
        0,0,0,0,-(2*E2*z*((h2^3-h1^3)/3))*((beta2(omiga))^2)*sin(beta2(omiga)*b),-(2*E2*z*((h2^3-h1^3)/3))*((beta2(omiga))^2)*cos(beta2(omiga)*b),(2*E2*z*((h2^3-h1^3)/3))*((beta2(omiga))^2)*sinh(beta2(omiga)*b),(2*E2*z*((h2^3-h1^3)/3))*((beta2(omiga))^2)*cosh(beta2(omiga)*b),((2*z/3)*(E1*(h1)^3+E2*((h2)^3-(h1)^3)))*((beta3(omiga))^2)*sin(beta3(omiga)*b),((2*z/3)*(E1*(h1)^3+E2*((h2)^3-(h1)^3)))*((beta3(omiga))^2)*cos(beta3(omiga)*b),-((2*z/3)*(E1*(h1)^3+E2*((h2)^3-(h1)^3)))*((beta3(omiga))^2)*sinh(beta3(omiga)*b),-((2*z/3)*(E1*(h1)^3+E2*((h2)^3-(h1)^3)))*((beta3(omiga))^2)*cosh(beta3(omiga)*b);
        -((2*z/3)*(E1*(h1)^3+E2*((h2)^3-(h1)^3)))*((beta1(omiga))^3)*cos(beta1(omiga)*a),((2*z/3)*(E1*(h1)^3+E2*((h2)^3-(h1)^3)))*((beta1(omiga))^3)*sin(beta1(omiga)*a),((2*z/3)*(E1*(h1)^3+E2*((h2)^3-(h1)^3)))*((beta1(omiga))^3)*cosh(beta1(omiga)*a),((2*z/3)*(E1*(h1)^3+E2*((h2)^3-(h1)^3)))*((beta1(omiga))^3)*sinh(beta1(omiga)*a),(2*E2*z*((h2^3-h1^3)/3))*((beta2(omiga))^3)*cos(beta2(omiga)*a),-(2*E2*z*((h2^3-h1^3)/3))*((beta2(omiga))^3)*sin(beta2(omiga)*a),-(2*E2*z*((h2^3-h1^3)/3))*((beta2(omiga))^3)*cosh(beta2(omiga)*a),-(2*E2*z*((h2^3-h1^3)/3))*((beta2(omiga))^3)*sinh(beta2(omiga)*a),0,0,0,0;
        0,0,0,0,-(2*E2*z*((h2^3-h1^3)/3))*((beta2(omiga))^3)*cos(beta2(omiga)*b),(2*E2*z*((h2^3-h1^3)/3))*((beta2(omiga))^3)*sin(beta2(omiga)*b),(2*E2*z*((h2^3-h1^3)/3))*((beta2(omiga))^3)*cosh(beta2(omiga)*b),(2*E2*z*((h2^3-h1^3)/3))*((beta2(omiga))^3)*sinh(beta2(omiga)*b),((2*z/3)*(E1*(h1)^3+E2*((h2)^3-(h1)^3)))*((beta3(omiga))^3)*cos(beta3(omiga)*b),-((2*z/3)*(E1*(h1)^3+E2*((h2)^3-(h1)^3)))*((beta3(omiga))^3)*sin(beta3(omiga)*b),-((2*z/3)*(E1*(h1)^3+E2*((h2)^3-(h1)^3)))*((beta3(omiga))^3)*cosh(beta3(omiga)*b),-((2*z/3)*(E1*(h1)^3+E2*((h2)^3-(h1)^3)))*((beta3(omiga))^3)*sinh(beta3(omiga)*b)]),i,optimset('display','off'));
end
ro1=root;
j_tem=1;
k_tem=1;
for i_tem=1:1999                 %去重根
    b_tem(i_tem)=ro1(i_tem+1);
end
b_tem(2000)=ro1(2000);
c_tem=b_tem-ro1;
c_tem_find_first= find( c_tem>0.1);
r_tem(j_tem)=ro1(c_tem_find_first(1));
r_tem(j_tem+1)=b_tem(c_tem_find_first(1));
j_tem=j_tem+2;

for i_c=c_tem_find_first(2):2000
    if c_tem(i_c)>0.1
        r_tem(j_tem)=b_tem(i_c);
        j_tem=j_tem+1;
    end
end
r_tem;
for i_re=1:j_tem-2
    root_return(i_re)=r_tem(i_re+1);
end
root_return;
ri=root_return/co