Vamsi Krishna Vegamoor
PhD, Mechanical Engineering

Modal Assurance Criterion (MAC)

Item 4a: A sample MAC plot generated by the MATLAB code I wrote.

This was a short project I worked on over the summer, for my professor Dr. Sami El-Borgi.

 

First, some brief background about Modal Assurance Criterion:

In Finite Element (FE) modelling, high order models are those with a large number of nodes. While these are more accurate representations of the real object, they are computationally intensive. Hence, research is always ongoing to reduce these to low-order models with fewer nodes. Now, these low order FE models almost always have lower fidelity than the large ones, but how do we tell how well they compare to the original FE model?

 

That's where the concept of Modal Assurance Criterion comes in. It utilizes the mass and stiffness matrices of the corresponding FE models and using a series of vector operations, creates an output matrix. Ideally, if the low - order model behaves just like the high order FE model, then all the diagonal terms in the matrix will be 1 and all the other terms will be 0. This, of course is never the case. (As you can see in the sample 3D graph in Item 4a, the off diagonal terms will not all be 0 and the diagonal terms will be close to, but not at 1). My task, set by the professor, was to create user-friendly code that could utilize ANSYS FE models and calculate MAC, thereby telling the user of the relative fidelity of the models.