Coding a Numerical Solution to the Multidegree of Freedom (MDOF) System Using Python

Deriving the equations of motion for a multi degree-of-freedom (MDOF) system. Solving by direct integration of the equations of motion using a time-marching solution implemented in Python.

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[BenCrews]

I had a lot of frustration with this one, because I didn't realize numpy.linalg.eigh is different than scipy.linalg.eigh. The input form is different, and it gives different values of a different shape than what we intend here! Hopefully others will see this if they're having issues! Good luck!

[CalumDouglas]

This is very good, I coded it in Python and it matches my own program in Octave. However I did notice that I could get some very slightly erronious mode shapes if I did "eigh(A)" (if A is the typical characteristic matrix) as oppose to eigh(K, M). Which is a slight mystery to me as in Octave this does not occur, anyway I guess the algorithms are slightly different for each program.

[CAFMuller]

Hey man, great video as always. Thank you for your hard work and high quality of content.

How would one go about finding the frequency response of such a system? Would a simple loop for the frequency do the trick? I can't quite see how that would work if damping was involved as well, for example.
Again, thank you very much.

[DEChacker]

Hello Mister, thank u very much for the video. Can u please explain why it is eigh(K, M)? Of which matrix will it calculate the eigenvalues and vectors?

[amirrahmanzadeh]

Thanks for the video, what should I do to plot the free vibration response should I set the F0 to zero? because then the response is only a horizontal line.

[nmuire]

So now I can find displacements and velocities . What could I do to get some accelaration data?