I'm dealing with a non-properly constrained mechanical model. I have to find the vibration properties of the system hence I'm dealing with a generalized eigenvalue problem of the following form:
$ (K-\omega^2M)\phi=0 $
Since the model is not properly restrained, it will have rigid body modes which is equivalent to eigenshapes having an eigenvalue of 0. I know the exact number of null eigenvalues (rigid body modes) that I must obtain.
I'm using the block Lancsoz solver of a commercial finite element code. I have the option of choosing the block size (0 to 16). I tried the code with different values and it gave me the correct number of null eigenvalues (the values are not actually 0 but very close to 0) when I used a block size of 12 or higher. With a block size that is lower then 12 I was getting a much lower number of null eigenvalues.
I tried to find more details on the internet but I couldn't find much help concerning the block size effect and how it helped me get the correct number of rigid body modes. Can someone explain how it works? I would also like to know if the number of rigid body modes must be a multiple of the block size.
Thank you