matlab code for eigenvalue problem

i need to solve eigenvalue problem for wave propagation in functionally graded rod functionally graded material composed of 2 or more other material in this problem,this rod composed of two material i have all of Initial values but i cant wrote matlab code for it

The problem is as follows: A=[A11,A12,A13;A21,A22,A23;A31,A32,A33] P=[pm1;pm2;pm3] M=[Mj,0,0;0,Mj,0;0,0,Mj]

A*P=(c^2)*M*P c is the eigen value and pmi are eigen vector

A11=(1/kH)^l*((C11^(l)*I3^l+2)+((l+1)*C11^(l)*I2^l+1)+((lC12^(l)-C22^(l))*I1(m)^l)-n^2*C66^(l)*I1(m)^l-C55^(l)*I1(m)^l+2+C11^(l)*K2(m)^l+2+C12^(l)*K1(m)^l+1)

A12=(1/kH)^l*((i*n*(C12^(l)+C66^(l))*I2(m)^l+1)-(i*n*(C22^(l)+C66^(l)-l*C12^(l))*I1(m)^l)+(i*n*C12^(l)*K1(m)^l+1))

A13=(1/kH)^l*((-i*(C55^(l)+C13^(l))*I2(m)^l+2)-(i*((1+l)*C13^(l)-C23^(l))*I1(m)^l+1)-i*C13^(l)*K1(m)^l+2)

A21=(1/kH)^l*((i*n*(C12^(l)+C66^(l))*I2(m)^l+1)+(i*n*((1+l)*C66^(l)+C22^(l))*I1(m)^l)+(i*n*C66^(l)*K1(m)^l+1))

A22=(1/kH)^l*((C66^(l)*I3(m)^l+2)+((1+l)*C66^(l)*I2(m)^l+1)-((1+l)*C66^(l)*I1(m)^l)-(n^2*C22^(l)*I1(m)^l)-(C44^(l)*I1(m)^l+2)+(C66^(l)*K2(m)^l+2)-(C66^(l)*K1(m)^l+1))

A23=(1/kH)^l*(n*(C44^(l)+C23^(l))*I1(m)^l+1)

A31=(1/kH)^l*((-i(C13^(l)+C55^(l))*I2(m)^l+2)-i(((1+l)*C55^(l)+C23^(l))*I1(m)^l+1)-i*C55^(l)*K1(m)^l+2)

A32=(1/kH)^l*(n*(C44^(l)+C23^(l))*I1(m)^l+1)

A33=(1/kH)^l*((C55^(l)*I3(m)^l+2)-n^2*(C44^(l)*I1(m)^l)-(C33^(l)*I1(m)^l+2)+((1+l)*C55^(l)*I2(m)^l+1)+(C55^(l)*K2(m)^l+2))

Mj=ro^(l)*(1/kH)^l*I1(m)^l+2

I1(m)^l=KR1/2*((g(m+1)*I1(m+1)^l-1)+(I1(m)^l-1)+(g(m)*I1(m-1)^l-1))

I2(m)^l=KR1/2*sqrt(2m+1)*((sqrt(2m+1)*I1(m-1)^l)+(sqrt(2m-5)*I1(m-3)^l)+(sqrt(2m-9)*I1(m-5)^l)+...)

I3(m)^l=KR1/2*sqrt(2m+1)*((sqrt(2m+1)*I2(m-1)^l)+(sqrt(2m-5)*I2(m-3)^l)+(sqrt(2m-9)*I2(m-5)^l)+...)

K1(m)^l=Qj(KR1)*(KR1)^l*Qm(KR1)

K2(m)^l=KR1/2*sqrt(2m+1)*((sqrt(2m+1)*K1(m-1)^l)+(sqrt(2m-5)*K1(m-3)^l)+(sqrt(2m-9)*K1(m-5)^l)+...)

%l run from 0 to 3

Qm(q1)=sqrt((2m+1)/KR1*Pm*(2q1-KR1)/KR1) %Pm,mth Legendre polynomial Qm(KR1)=sqrt((2m+1)/KR1*Pm %Pm,mth Legendre polynomial

g(m)=m/(2m-1)*(2m+1) %m run from 0 to 8

Valid values:

C11^(0)=46.8419

C11^(1)=-9.4828

C11^(2)=0.8735

C11^(3)=-0.2319

C12^(0)=9.2556

C12^(1)=2.8590

C12^(2)=0.0797

C12^(3)=-0.1936

C44^(0)=18.7909

C44^(1)=-6.1663

C44^(2)=0.3938

C44^(3)=-0.0185

ro^(0)=-3.4260

ro^(1)=5.7960

ro^(2)=0

ro^(3)=0

C22=0

C13=0

C55=0

C66=0

C23=0

C33=0

R1=H=0.2m

0<q1<KR1

KR1=KH=0,1,2,3,...,20

n=0,1

i=sqrt(-1)

Answer 1

[Hank]

Try simplifying the problem you're having instead of dumping equations. I went cross-eyed and I don't know what you want.