Learning Forum

[Md_Salem]

Hello everyone,

In an older post, I was asking about some methods to extract the eigenvectors of modal analysis in order to proceed with further analysis, such as orthogonality checks and the modal assurance criterion (MAC) for this modal analysis. Gratefully, some fellows showed me the example in the title. In this example, check orthogonality by multiplying the (transpose of the modal matrix*mass matrix*modal matrix) to receive the dentity matrix !!

In the text books, the orthogonality check for two vectors is done by the dot product of those two vectors; if they are orthogonal, then their dot multiplication should be equal to zero. when I tried to do this with the vectors of (SOLVPhi) in the shown example, but unfortunately it didn't fulfill the condition of the orthogonality, which should (according to text books) be zero.

Also, it will be greatly appreciated if there is any way to use MAC for these eigenvectors.

Regards.

[mrife]

Hi Md_Salem

You will need to show your work and prove this.  I just tried with Verfication Manual model 61 using version 2023R2 of Mechanical APDL and PhiTMPhi was the identity matrix with off diagonal terms on the order of 1E-12 which is close enough to zero for engineering needs (diagonal terms exactly 1).

Mike

[Md_Salem]

 

Dear Mike,

appreciated for your concern.

I have already tried to do it with (PhiTMPhi) and I had the identity matrix just as you did.

The purpose of my inquiry is to address the definition of orthogonal vectors as presented in textbooks, which states that orthogonal vectors are those whose dot product yields zero. This condition results in the identity matrix when all the eigenmodes of the matrix Phi are multiplied by themselves via dot product. However, in the context being discussed, this condition does not hold. I would like to inquire about potential scholarly references pertaining to the relationship denoted as PhiTMPhi. Alternatively, could you provide any APDL code that may be utilized to compute the modal assurance criterion (MAC) for the aforementioned modes?

Regards

 

[mrife]

Hi Md_Salem

I think you misunderstood: please see the Mechanical APDL Help; Ansys Parametric Design Language Guide; APDL Math; 4.8 APDL Math Examples, example 4.1.  Use the procedure shown there.  It should return the identity matrix.  If the mode shapes are not orthogonal then some off diagonal terms will not be zero (or very small as I described above.).

For the MAC see the MAPDL Help; Basic Analysis Guide; Chapter 7 Additional Post Processing -> 7.3.8 (depending on version may be slightly different) Comparing Nodal Solutions from Two Models or From One Model and Experimental Data (RSTMAC).  It has examples including the APDL code.

Mike