Hi,

I'd like to solve the following equation involving matrices for unknown v and θ:



After inputting it in the format used by the Maxima plug-in I get the "no result" message:



Am I doing something wrong ?

Matrix equation.sm (8 KiB) downloaded 36 time(s).

Wrote

Am I doing something wrong ?

Your setup is not correct.

I think the problem is that the units don't match. Compare the units of the components of the two terms inside the brackets that multiply the [v; theta] vector.

Wrote

I think the problem is that the units don't match.
Compare the units of the components of the two terms inside the brackets
that multiply the [v; theta] vector.

FindRoots ignores Units. Code the image first.

Solve FindRoots Complex Forum.sm (11 KiB) downloaded 28 time(s).

Wrote

Your setup is not correct.

Thank you, I didn't know that I should use the Nonlinear Solvers plug-in instead of the Maxima one.

It works now but the result is surprising. It should be something like v = - 0.021020 for the real part with this input data.

Wrote

I think the problem is that the units don't match. Compare the units of the components of the two terms inside the brackets that multiply the [v; theta] vector.

I also suspected the units initially but it didn't work without them either.

I also suspected the units initially but it didn't work without them either.

In order to be able to add the two terms they must have the same units. However, omega^2*L doesn't have the same units as EI/L^3. The omega^2*... term seems to be missing a linear mass density (kg/m).
The fact that you might be able to get a numerical result by simply removing the units is irrelevant.

Wrote

In order to be able to add the two terms they must have the same units. However, omega^2*L doesn't have the same units as EI/L^3. The omega^2*... term seems to be missing a linear mass density (kg/m).
The fact that you might be able to get a numerical result by simply removing the units is irrelevant.

Right, I was wondering why density/mass is not included in that equation. Especially since it's included in the equation for tension (the one here is for bending): https://code-aster.org/V2/doc/v13/en/man_v/v2/v2.06.101.pdf

Maybe it's a typo and the density should be added before the first omega. Or omega means something different than I assumed (angular frequency).

Edit: I tried calculating mass per unit length based on the density and cross-section area provided in the document and then multiplying it by omega^2 but the result is v = 0,0175 which is still far from the expected value.

Besides correction of the unit mismatch, Solve seems to want the matrix equation in homogeneous form.


Matrix equation_Kr.sm (14 KiB) downloaded 24 time(s).

Hi. Another way.



Best regards.
Alvaro.