Hard to give an example that would be relevant to your particular activities, but violin makers sometimes use it in a practical way.

When you make a wooden soundboard you can visualize its deformation eigenfunctions (or rather its zeros) and proper frequencies using a speaker and sand:

https://www.youtube.com/watch?v=_l2Uh5EVxB8

And they use it to "tune" the soundboard somewhat as far as I understand it ?

Also, for the strict "anything described in Fourier" proposition, you can draw homer Simpson with epicycles with it:
https://www.youtube.com/watch?v=slfS7j_7L6s

So I guess all the 1400's astronomy was using it somewhat