You can also solve the same frequency response problem using the modal method. The same remarks as for the Time-dependent Modal analysis above are relevant.
LEGENDS Y
LEGENDS Z
Solved with COMSOL Multiphysics 4.2a
Results and Discussion
In Figure 12 below, the results from the modal frequency response analysis are overlaid on the results from the previous direct frequency response analysis (see Figure 11).
The curves are almost indistinguishable. The response is to a large degree controlled by the lowest eigenmodes, which are used in the modal analysis. The modal method is however more effective in terms of computer resources.
Figure 12: Displacement amplitudes vs. excitation frequency for direct and modal frequency-response analyses.
Modeling Instructions
S O L I D M E C H A N I C S
Static Load
In the Model Builder window, right-click Model 1>Solid Mechanics>Static Load and choose Disable.
Boundary Load 4
1 Right-click Solid Mechanics and choose Boundary Load.
2 In the Model Builder window, right-click Boundary Load 4 and choose Rename. 3 Go to the Rename Boundary Load dialog box and type Modal Frequency Load in
the New name edit field.
Solved with COMSOL Multiphysics 4.2a
38 | V A R I O U S A N A L Y S E S O F A N E L B O W B R A C K E T © 2 0 1 1 C O M S O L
4 Click OK.
5 Select Boundary 29 only.
6 Go to the Settings window for Boundary Load.
7 Locate the Force section. Specify the FA vector as
M O D E L W I Z A R D
1 In the Model Builder window, right-click the root node and choose Add Study. 2 Go to the Model Wizard window.
3 In the Studies tree, select Custom Studies>Empty Study. 4 Click Finish.
S T U D Y 7
1 In the Model Builder window, right-click Study 7 and choose Rename. 2 Go to the Rename Study dialog box and type Study 7 (Modal Frequency
Response) in the New name edit field.
3 Click OK.
S T U D Y 7 ( M O D A L F R E Q U E N C Y R E S P O N S E )
Step 1: Frequency-Domain Modal
1 In the Model Builder window, right-click Study 7 (Modal Frequency Response) and choose Study Steps>Frequency-Domain Modal.
2 Go to the Settings window for Frequency-Domain Modal.
3 Locate the Study Settings section. In the Frequencies edit field, type range(350,10,650).
Solver 7
1 In the Model Builder window, right-click Study 7 (Modal Frequency Response) and choose Show Default Solver.
2 Expand the Study 7 (Modal Frequency Response)>Solver Configurations node.
3 Right-click Study 7 (Modal Frequency Response)>Solver Configurations>Solver 7 and choose Rename.
linper(3)[MPa] X
0 Y
linper(3)[MPa] Z
Solved with COMSOL Multiphysics 4.2a
4 Go to the Rename Solver dialog box and type Modal Frequency-Domain Sequence in the New name edit field.
5 Click OK.
Modal Frequency-Domain Sequence
1 In the Model Builder window, expand the Study 7 (Modal Frequency Response)>Solver Configurations>Modal Frequency-Domain Sequence node, then click Modal Solver 1. 2 Go to the Settings window for Modal Solver.
3 Locate the Eigenpairs section. From the Solution list, select Eigenfrequency Sequence. 4 In the Model Builder window, right-click Study 7 (Modal Frequency Response) and
choose Compute. R E S U L T S
Data Sets
1 In the Model Builder window, right-click Results>Data Sets>Solution 7 and choose Rename.
2 Go to the Rename Solution dialog box and type Modal Frequency-Domain Solution in the New name edit field.
3 Click OK. Stress (solid)
1 In the Model Builder window, expand the Stress (solid) node, then click Surface 1. 2 Go to the Settings window for Surface.
3 Locate the Expression section. From the Unit list, select MPa.
Solved with COMSOL Multiphysics 4.2a
40 | V A R I O U S A N A L Y S E S O F A N E L B O W B R A C K E T © 2 0 1 1 C O M S O L
4 Click the Plot button.
5 In the Model Builder window, right-click Stress (solid) and choose Rename.
6 Go to the Rename 3D Plot Group dialog box and type Modal Frequency-Response Stress Contour in the New name edit field.
7 Click OK.
Frequency Response Displacement Graphs Reproduce the plot in Figure 12 as follows:
1 In the Model Builder window, right-click Results>Frequency Response Displacement Graphs and choose Point Graph.
2 Go to the Settings window for Point Graph.
3 Locate the Data section. From the Data set list, choose Modal Frequency-Domain Solution.
4 Select Point 30 only.
5 In the upper-right corner of the y-Axis Data section, click Replace Expression. 6 From the menu, choose Solid Mechanics>Displacement>Displacement amplitude
(Material)>Displacement amplitude, X component (solid.uAmpX).
7 Locate the Coloring and Style section. Find the Line style subsection. From the Color list, choose Blue.
8 From the Line list, choose Dashed.
Solved with COMSOL Multiphysics 4.2a
9 Find the Line markers subsection. From the Marker list, choose Asterisk. 10Locate the Legends section. Select the Show legends check box.
11From the Legends list, choose Manual. 12In the table, enter the following settings:
13In the Model Builder window, right-click Frequency Response Displacement Graphs and choose Point Graph.
14Go to the Settings window for Point Graph.
15Locate the Data section. From the Data set list, choose Modal Frequency-Domain Solution.
16Select Point 30 only.
17In the upper-right corner of the y-Axis Data section, click Replace Expression. 18From the menu, choose Solid Mechanics>Displacement>Displacement amplitude
(Material)>Displacement amplitude, Y component (solid.uAmpY).
19Locate the Coloring and Style section. Find the Line style subsection. From the Color list, choose Green.
20From the Line list, choose Dashed.
21Find the Line markers subsection. From the Marker list, choose Asterisk. 22Locate the Legends section. Select the Show legends check box.
23From the Legends list, choose Manual. 24In the table, enter the following settings:
25In the Model Builder window, right-click Frequency Response Displacement Graphs and choose Point Graph.
26Go to the Settings window for Point Graph.
27Locate the Data section. From the Data set list, choose Modal Frequency-Domain Solution.
28Select Point 30 only.
29In the upper-right corner of the y-Axis Data section, click Replace Expression.
LEGENDS X (modal)
LEGENDS Y(modal)
Solved with COMSOL Multiphysics 4.2a
42 | V A R I O U S A N A L Y S E S O F A N E L B O W B R A C K E T © 2 0 1 1 C O M S O L
30From the menu, choose Solid Mechanics>Displacement>Displacement amplitude (Material)>Displacement amplitude, Z component (solid.uAmpZ).
31Locate the Coloring and Style section. Find the Line style subsection. From the Color list, choose Red.
32From the Line list, choose Dashed.
33Find the Line markers subsection. From the Marker list, choose Asterisk. 34Locate the Legends section. Select the Show legends check box.
35From the Legends list, choose Manual. 36In the table, enter the following settings:
37Click the Plot button.