Finding roots of a matrix equation

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kimi 2020-7-17

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https://ww2.mathworks.cn/matlabcentral/answers/566766-finding-roots-of-a-matrix-equation

评论： kimi 2020-7-24

Hello,

I'm having trouble getting roots for this matrix. The example has to do with finding the natural frequency and mode shapes of a a simple rigid rotor system on anisotropic flexible supports. I have the formula, answer, and polynomial from the matrix equation just struggling to find the roots. Please help.

The question is example 3.6.1(a) finding roots s1-8.

I believe im solving for q and q` but im not sure how to put this in matlab. Or maybe us

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回答（1 个）

Devineni Aslesha 2020-7-20

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https://ww2.mathworks.cn/matlabcentral/answers/566766-finding-roots-of-a-matrix-equation#answer_468105

Refer the roots documentation from the given link

https://www.mathworks.com/help/matlab/ref/roots.html

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kimi 2020-7-23

>> G

G =

0 0 0 0

0 0 0 0.6134

0 0 -0.6134 0

>> M

M =

122.6800 0 0 0

0 122.6800 0 0

0 0 2.8625 0

0 0 0 2.8625

>> K

K =

2300000 0 0 75000

0 2300000 -75000 0

0 -75000 143750 0

75000 0 0 143750

//418.88 = 4000 * (2*pi/60) = omega reference page 97

A = [G*(418.88) M; M zero]

A =

0 0 0 0 122.6800 0 0 0

0 0 0 0 0 122.6800 0 0

0 0 0 256.9410 0 0 2.8625 0

0 0 -256.9410 0 0 0 0 2.8625

122.6800 0 0 0 0 0 0 0

0 122.6800 0 0 0 0 0 0

0 0 2.8625 0 0 0 0 0

0 0 0 2.8625 0 0 0 0

>> B = [K zero; zero -M]

B =

1.0e+06 *

2.3000 0 0 0.0750 0 0 0 0

0 2.3000 -0.0750 0 0 0 0 0

0 -0.0750 0.1437 0 0 0 0 0

0.0750 0 0 0.1437 0 0 0 0

0 0 0 0 -0.0001 0 0 0

0 0 0 0 0 -0.0001 0 0

0 0 0 0 0 0 -0.0000 0

0 0 0 0 0 0 0 -0.0000

///zero is a 4x4 zero matrix

>> s = eig(B,-A)

s =

1.0e+02 *

0.0000 + 2.2532i

0.0000 - 2.2532i

0.0000 + 2.2510i

0.0000 - 2.2510i

0.0000 + 1.3508i

0.0000 - 1.3508i

0.0000 + 1.3508i

0.0000 - 1.3508i

Can you see anything im doing wrong to not get the same roots displayed in pg100. The only thing I can think of is that my B matrix is reduced too much on the lower right corner.

Walter Roberson 2020-7-24

s = eig(B,A) but before it was eig(B, -A)

kimi 2020-7-24

That was a mistake the values aren't that different

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