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Hello Sean,
First of all, cheers again for your incredible lectures and your effort. It really made me understand step by step the real picture behind it thanks to incredible teaching skills from your side and going into the basics to advanced level.
My question is the following ;
We can make sure that [M] matrix is diagonal and identity matrix (I) is formed after the normalization process for mass matrix i.e I=[(1,0,0), (0,1,0), (0,0,1)]
On the other hand, we can only guarantee for [K] matrix that there will be diagonal matrix formed after the normalization process completed for [K] matrix, but we cannot guarantee whether the resulting product will be Identity Matrix or not.
Why is that ? Time Range In the video for the question stated above: 15:38 -16:20
Cheers,
Sincerely,
Burak
Burak,
Sorry about the delay in replying to you…I’ve just published a new course, so it’s been a hectic week!
Interesting question…
When we mass normalise the modal matrix and perform the decoupling operation (equation 8 in lecture 23), as you say, we get the identity matrix. If we perform the same operation on the stiffness matrix (equation 9), we also get a diagonal matrix. But what I neglected to say in the lecture is that the resulting matrix is sometimes called the spectral matrix, and its diagonal elements are actually the eigenvalues - the square of the natural frequencies of the uncoupled systems.
Seán