I'm working on a plate vibration problem using eigenvalue analysis. The dependent variables are u, v, w and arx, ary, arz. I export the mode profiles sampled at a grid and for some reason the modes are not orthogonal. The grid contains 100x100 points, which should be sufficient to ensure orthogonality.
i.e.: The sum u_ki*u_kj + v_ki*v_kj + w_ki*w_kj + arx_ki*arx_kj +ary_ki*ary_kj +arz_ki*arz_kj (Where k is the grid point, and goes between 0 and 200*200-1) and i/j are mode numbers. For i different than j this sum is not zero (and not "very small").
This is causing me some trouble as I expected the mode profiles to be orthogonal, and it's required for my subsequent calculations.
Any help or lead on what's going on would be greatly appreciated.
i.e.: The sum u_ki*u_kj + v_ki*v_kj + w_ki*w_kj + arx_ki*arx_kj +ary_ki*ary_kj +arz_ki*arz_kj (Where k is the grid point, and goes between 0 and 200*200-1) and i/j are mode numbers. For i different than j this sum is not zero (and not "very small").
This is causing me some trouble as I expected the mode profiles to be orthogonal, and it's required for my subsequent calculations.
Any help or lead on what's going on would be greatly appreciated.