Simcenter 3D Solutions Pre-Test and Mode Correlation with bungee suspension

Initial wireframe

When doing correlation between test and FE data, it is important that both the test and FE model make use of the same boundary conditions, as the boundary conditions will have a significant influence on the mode shapes and frequencies. As it can be difficult to approximate rigid constraints in a test setup, it is common to opt for free-free conditions instead. Free-free conditions are very easy to attain in FE. In a test setup, the free-free condition is approximated by suspending the structure using bungees.
 
If we consider these free-free conditions in the test campaign, this also means that free-free conditions should be used when performing the pre-test analysis. Based on the free-free modes, a set of optimal sensor locations can be determined. Based on these locations, you can then create a wireframe representation of the model, using the test analysis reference solution. This test analysis reference solution not only generates the wireframe, it also reduces the FE modes to the selected measurement locations. Once the pre-test analysis is completed, we have an initial wireframe, which will act as a reference.
 

Including bungees

• Make the FEM file the work and displayed part
• Go to the "Nodes and Elements" tab
• In the "Elements" section, click on "Element Create"
• Set the element family to "0D"
• Set the element type to "CBUSH(grounded)"
• Click the nodes of the structure, where the bungees would be attached
• Click ok
• Right click the newly created CBUSH mesh collector in the simulation navigator
• Click on "Edit"
• Edit the PBUSH property
• Set the stiffness for the relevant DOF

For the given example, you could for example select 4 attachment points, representing bungees with 10 kN/m stiffness.
 

• Make the SIM file the work and displayed part
• Right click the original modal solution - select "Clone"
• Rename the solution to "Soft Bungees"
• Solve the solution

• Make the FEM file the work and displayed part
• Right click the CBUSH mesh collector in the simulation navigator
• Click on "Edit"
• Edit the PBUSH property
• Change the stiffness with a factor 40 to 400 kN/m
• Make the SIM file the work and displayed part
• Right click the original modal solution - select "Clone"
• Rename the solution to "Stiff Bungees"
• Solve the solution

Reviewing the influence 

We now have 3 solutions: the free-free modes, the modes using soft bungees and the modes using stiff bungees. To compare all 3, we can create two correlation solutions and plot the MAC matrices.
 

• Right click on the Sim file
• Select "New solution process" - Shape Correlation
• Select the test analysis reference solution as the reference solution 
• Select the "Soft Bungees" solution as work solution
• Click ok
• Right click the "Shape Correlation Metrics" and plot the MAC matrix

The results are shown below. 

On the left side, we can see the influence of the softer bungees. In this case, you can notice that the flexible modes still show a very good correlation, and that only the 6 rigid body modes are actually affected. You can see that 3 out of 6 modes still occur at 0 Hz. In addition, there are 3 rigid body modes at low, but non-zero frequencies. Although 3 of the 6 modes now occur at a non-zero frequency, they together still represent the rigid behavior of the structure.  

To demonstrate this, we can consider doing the correlation, defining mode clusters for the rigid body modes.
 

• Right click on "Shape Pairing"
• Toggle on the option "Define Mode Clusters" - click ok
• Right click "Mode Clusters" in the simulation navigator - select "Edit"
• Select the 6 first reference modes, select the 6 first work modes - click "Create" - click "Ok"
• Update the solution
• Right click on "Shape Correlation Metrics" - Click on "Plot MAC"
• Plot the MAC matrix

The result is shown on the right side. We can see, that if Simcenter 3D can create a linear combination of the rigid body modes, that we get a nicely matching MAC matrix. This indicates that the new rigid body modes are simply a linear combination of the original ones, and that they span the same modal subspace. 
 
In addition, we can check the simulation details, to review the residue calculated for the mode cluster. We can see that in this case, the residual error is low. This typically gives confidence that the mode clusters were selected correctly: each new mode lies (almost) entirely in the modal subspace of the 6 original ones.  
   
We can now repeat these same steps, but for the stiffer bungees. 
 

• Right click on the Sim file
• Select "New solution process" - Shape Correlation
• Select the test analysis reference solution as the reference solution 
• Select the "Stiff Bungees" solution as work solution
• Click ok
• Right click the "Shape Correlation Metrics" and plot the MAC matrix

The results are once again shown below. 

On the left side, we can see the influence of the stiffer bungees. In this case, you can see that the rigid body modes get affected once again. Similarly, we still see 3 of the rigid body modes. However, whereas with the softer bungees 3 additional rigid body modes were present at non-zero frequencies, in this case, we see 3 new flexible modes showing up. In addition, we can also see that of the 10 flexible modes, 6 remain relatively similar, while 4 modes are altered.

If we want to check whether the first 6 modes of the new mode set are still a linear combination of the original rigid body modes, we can once again try to cluster the modes. On the right side, we can see result of the clustering.
 

• Right click on "Shape Pairing"
• Toggle on the option "Define Mode Clusters" - click ok
• Right click "Mode Clusters" in the simulation navigator - select "Edit"
• Select the 6 first reference modes, select the 6 first work modes - click "Create" - click "Ok"
• Update the solution
• Right click on "Shape Correlation Metrics" - Click on "Plot MAC"
• Plot the MAC matrix

Although the rigid body modes seem to have a decent correlation, checking the residual error shows a relatively high error for a couple of the modes. As such, it is an indication that selection of the clusters is not really valid. So even though the MAC matrix shows a reasonable result, the error shows that the first 6 new modes do not entirely fall within the same modal subspace as the 6 original modes
 
In addition, as we are mostly interested in the flexible modes, we can see that the stiff bungees also have an influence on 4 of the flexible modes as well. In case these stiffer bungees would be used in the same configuration during the test campaign, then we can already expect that the correlation between the test and the free-free FE modes would not be good. 

In this case, it is a good idea to include the suspension of the structure in the FE model, when doing the test-FE correlation. By doing so, the FE model will match the test setup more closely, which should lead to better correlation results. 

The same can apply for the pre-test analysis, as it was based on the assumption of free-free modes. However, before starting from scratch, we can also check whether the current wireframe still captures the new modes sufficiently.
 

Checking sensor selection

• Right click on the Sim file
• Select "New solution process" - Pre-test Planning
• Select the mode set with the stiff bungees
• Click ok
• Right click the "Required/Initial DOF"
• Click "Edit"
• Use the selection method "Related Nodes"
• Select your original wireframe from the initial pre-test 
• Click ok

• Right click the "Required/Initial DOF" - Select "Correlate"
• Plot the MAC Matrix