Eigenvectors in Stroh Formalism

[FerMedina]

Hi, I'm trying to describe the Stroh formalism for anisotropic plates and I can't solve the eigenvectors for an eq. of the type " (A + B*l + C*l^2) * V = 0 ", where A, B and C are 3x3 matrix. I find solutions for l via solve and float, or polyroots if I don't use units with the matrix. But I can't find the associated V. If use find i get no result. If use minerr the results vary with the initial guess value.
I could definitely use your help with this!

I'm attaching a short version of the worksheet.
Thanks a lot.

[FerMedina]

Hi, so I keep trying to understand what I'm doing wrong. I'm even wondering whether it is wrong or not. I've checked that polyroots works better when I use companion matrix method. the result turns out to be more similar to that reached by solve and float.

The eigenvalue "l" is complex, and, as far as I know, that's likely to be the reason for what's going on. Following the files in the forum, I've worked out eigenvectors through solve blocks. it works just fine with any real guess values when the eigenvalues and eigenvectors are real. however, as soon as I insert a complex guess value, even if if eigenvals and eigenvecs are real, the solve block gives complex results for the eigenvectors, each time different as i change the guess value.

so now that the whole problem is complex, how do I know if the result is right or even accurate?

[FerMedina]

Hi again, I'm sorry, I was so focussed on the eigenvalue problem, that I didn't search thoroughly enough on the being complex issue. I just understood that the results vary with the initial guess value because the eigenvectors obtained are multiplied by different unit complex number.

It's funny though that Find won't work yet with the solve block. I'm still using minerr.

Do you think I'll drag a significant error for the rest of the formulation based on the eigenvectors?

[FerMedina]

well, i found out that the minerr doesn't even provide normalized eigenvectors, even though it's in the solve block. why isn't the find function working? is it because of the units?

can anybody please help me?

[RichardJ]

It took me much longer than it should have to figure out what the problem was, because you set the values of TOL and CTOL to completely ridiculous numbers! Why did you set them smaller than the computer roundoff of the numeric computations? There is no way Find could converge for any problem when CTOL is set to 10^-20!

You also have a scaling problem. I think you are mentally thinking of the numbers in terms of GPa, but Mathcad isn't. Mathcad stores them scaled to Pa.

[PhilipOakley]

Fernando,

I suspect that there aren't many who are experts on Stroh Formalism. I had to look it up <smiley>.

If you can simplify the problem to be the part where Minerr and Find aren't working as you would expect then I think that you will be able to get a response.

The deeply nested 'vectors' makes it hard for those not into Stroh to understand what is being asked of the system.

There are some known issues with Minerr and Find, which aren't errors per se, rather there are particular conditions that happen, some not explained in the documentation....

Philip

[pnav]

Dear fernando,

please check that attached are solutions for your problem ( first row eignevalues, second row eigenvector associated)

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pierre navidi