How can i solve this system ?

Hi

To determine the damping ratio (psij and psik ), i have to solve the attached system where all other name

are constant.

How can i solve this system ?

[Jan]

The attached image does not contain any "psi"s. Do you mean zeta or omega? Do you want to solve this symbolically or numerically?

What have you tried so far? Which problems occur? Is this a homework question? We should know the last detail, because this demands for another kind of answering.

[Mallouli Marwa]

I mean zeta

[Mallouli Marwa]

I want to solve it numerically.

Answer 1

[Torsten]

A = 2*omegaj*omegak/(omegaj^2-omegak^2)*[Y*I/omegak -Y*I/omegaj ; -m*omegak m*omegaj];
b = [cs*I ; ca];
zeta = A\b;
zetaj = zeta(1);
zetak = zeta(2);

Best wishes

Torsten.

[Mallouli Marwa]

Hi How can i stock zetaj and zetak in two vectors ?

ca_m = 19.295;

cs_I = 2.93e-6;

for i=1:8

A = 2 * wr(i)* wr(i+1) / (wr(i)^2 - wr(i+1)^2) * [1/ wr(i+1) -1/ wr(i) ; -wr(i+1) wr(i)];

b = [cs_I ; ca_m];

zeta = A\b;

zetaj = zeta(1);

zetak = zeta(2);

end

[Torsten]

zetaj(i)=zeta(1);
zetak(i)=zeta(2);

Best wishes

Torsten.

[Mallouli Marwa]

For this loop i obtain this error :

Warning: Matrix is singular, close to singular or badly scaled.

Results may be inaccurate. RCOND = NaN.

In program at 5 (zeta)

Please help me.

for i=1:10

      for k=1:10

      A = 2* wr(i)*wr(k)/(wr(i)^2-wr(k)^2)*[1/wr(k)  -1/wr(i) ; -wr(k) wr(i)];

      b = [cs_I ; ca_m];

      zeta = A\b;

      zetaj(k)=zeta(2);

      zetak (i)=zeta(1);

      end

    end

[Torsten]

If abs(wr(i))=abs(wr(k)), your matrix A becomes singular and you won't get a solution.

This will at least be the case if i=k in your nested-loop construction.

Best wishes

Torsten.

[Mallouli Marwa]

Please how can i correct this error ?

Answer 2

[Torsten]

Hint:

The inverse of

[a b ; c d]

is

1/(a*d-b*c)*[d -b; -c a]

Best wishes

Torsten.