Arizona State University
In the Fall, I was teaching the graduate Advanced Structural Dynamics class to a group of graduate students, both full time students and part time ones from local companies. A sizable part of the course focused on "component modal synthesis" methods for the modeling of complex structures composed of multiple components. I usually cover 4 different methods. The first two methods rely on free boundary modes, either alone (the "naive" method as I call it) or with attachment modes. The last two approaches are the Craig-Bampton and the Benfield and Hruda methods. My experience with this material has been that it involves difficult concepts and that the benefits/disadvantages of the various approaches are not very obvious to students. Typically, I have discussed these topics with simple models for which hand computations can be carried out, e.g. with lumped mass models, but it is a pretty dry presentation and the purpose/strengths of this process are not easily grasped. This time, I carried out the classical presentation but decided to illustrate it with a Nastran example.
Figure 1. Two cantilevered plates (α and β) connected at 4 nodes
The concepts did seem to catch on better and accordingly, I opted to make a sizable part of the grade based on a project to demonstrate the strengths and weaknesses of each approach. I gave the students the Nastran model of two cantilever rectangular plates of the same aspect ratio but of different sizes connected to each other over a few nodes, see Fig. 1. I then asked them to proceed with a convergence study of the natural frequencies and mode shapes with respect to the number of modes kept in the two parts. Many of them were already familiar with Nastran, some were not but they caught on very quickly and used the SOL 103 and SOL 101 to generate the natural modes and constraint and attachment modes and regenerate the frequencies and modes of the assembled reduced order model. They then compared these frequencies and modes with those of the original structure for different number of modes to generate convergence plots such as those shown in Figure 2. I asked the students to make a short presentation of their results during which I was able to assess how well they had understood the differences. It was amazing how much better they had understood these methods as compared to students of previous years. Clearly, the hands-on Nastran project did the trick!
Figure 2. Some of the convergence results obtained by the students for the structure of Fig. 1 based on Nastran SOL 103 and SOL 101 analyses.
Prof. Marc P. Mignolet
School of Mechanical, Aerospace, Chemical, and Materials Engineering
Arizona State University, Tempe, AZ 85287-6106
Tel. (480) 965-1484 ; Fax. (480) 727-9321