MAE7031-B Assignment Help Sheet

MAE7031-B Assignment Help Sheet
The aim of this help sheet is to give you guidance on your results from ABAQUS, Matlab and
the experimental testing. There are also some comments on what to look for in your data.
FEA Results
Figure 1 shows the mode shapes that you should be extracting from your FE model. They
are diametral mode shapes which means that the shape can be divided by drawing diametral
lines across the disc. A 2 diameter mode of vibration is therefore where the disc has been
split into 2 ‘diameters’, resulting in 4 antinodes.
The mode shapes appear in pairs – the frequencies are closely spaced – so it is acceptable to
take an average of the two values.
There will be other mode shapes, but these can be ignored as they are not relevant to your
2 Diameter 3 Diameter 4 Diameter
5 Diameter 6 Diameter 7 Diameter
8 Diameter 9 Diameter 10 Diameter
Figure 1: Example diametral mode shapes
MAE7031-B Assignment Help Sheet
The mode shapes are formed from antinodes (the peaks of the waveform which vibrate up
and down) and nodes (the stationary points) – these are shown in Figure 2 below.
2 Diameter 9 Diameter
The vibration of the disc in these mode shapes is out-of-plane. The FRF data recorded from
the ‘tap’ testing of the disc measured acceleration in the out-of-plane direction. The
predicted (simulated) and measured results can be plotted against each other to validate the
accuracy of the predictions. You can plot a graph of mode shape against frequency for your
FEA results. It should look similar to Figure 3.
It is expected that you undertake a mesh sensitivity study (also known as mesh
independence) to ensure that the results are insensitive to the quality and density of the
mesh elements. To do this you can plot a particular result against the number of elements
and determine if the results are stable.
Figure 3: FEA results
Figure 2: Out-of plane

MAE7031-B Assignment Help Sheet
Experimental Results
The results from the experimental “tap” testing of the brake disc will look similar to Figure 4
below. Your frequency values may be different to this example. Each peak frequency will be
an out of plane natural frequency. You are only interested in the major frequencies – these
relate to the diametral modes.
The first frequency will be a 2-diameter (2D) mode of vibration
The next frequency will be 3-diameter (3D) and so on as below.
How many modes are visible will depend upon the quality of your data. You can
see below that the 9-diameter mode is difficult to discern from the other excited
4D 5D
Figure 4: Experimental results

MAE7031-B Assignment Help Sheet
Estimating Damping Using the Half-power bandwidth method:
Using the FRF data as shown in figure 5 and by assuming damping is small, the following
equation can be used to estimate damping:

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