Modal Analysis Examples Using Realistic Models¶
Analysis Models¶
Table 9.4.1 lists the verification examples using realistic models for modal analysis. Among these, the model geometries for EX07 (turbine rotor) and EX08 (spring) are shown in Figures 9.4.1 and 9.4.2. The other model geometries are the same as those used by the corresponding elastic static analysis verification examples shown earlier. A separate direct solver is required to run the examples using element types 731 and 741.
Table 9.4.1 Verification examples using realistic models for modal analysis
| Case Name | Element Type | Verification Model | Number of Nodes | Degrees of Freedom |
|---|---|---|---|---|
| EX06 | 342 | Turbine blade | 10,095 | 30,285 |
| EX07 | 361 | Turbine rotor | 127,440 | 382,320 |
| EX08 | 342 | Spring | 78,771 | 236,313 |
| EX09 | 741 | Cylindrical shell | 10,100 | 60,600 |
| EX10A | 731 | Wine glass (coarse) | 7,240 | 43,440 |
| EX10B | 731 | Wine glass (medium) | 48,803 | 292,818 |
Figure 9.4.1 Turbine rotor (EX07)
Figure 9.4.2 Spring (EX08)
Analysis Results¶
The mode shapes and natural frequencies are shown below.
EX06 Turbine Blade¶
 |  |
| (a) Mode 1 (1170 kHz) | (b) Mode 2 (3250 kHz) |
 |  |
| (c) Mode 3 (4130 kHz) | (d) Mode 4 (4140 kHz) |
 | |
| (e) Mode 5 (8210 kHz) |
Figure 9.4.3 EX06 Turbine Blade Mode Shapes
EX07 Turbine Rotor¶
 |  |
| (a) Mode 1 (1067 Hz) | (b) Mode 2 (1072 Hz) |
 |  |
| (c) Mode 3 (1072 Hz) | (d) Mode 4 (1093 Hz) |
 | |
| (e) Mode 5 (1093 Hz) | |
Figure 9.4.4 EX07 Turbine Rotor Mode Shapes
EX08 Spring¶
| Mode 1 (445 Hz) | Mode 2 (446 Hz) | Mode 3 (908 Hz) |
 |  |  |
| Mode 4 (985 Hz) | Mode 5 (1819 Hz) | |
 |  |
| FrontISTR | NASTRAN | |
|---|---|---|
| 1 | 445 Hz | 445 Hz |
| 2 | 446 Hz | 446 Hz |
| 3 | 908 Hz | 908 Hz |
| 4 | 985 Hz | 986 Hz |
| 5 | 1810 Hz | 1810 Hz |
Figure 9.4.5 EX08 Spring Mode Shapes
EX09 Cylindrical Shell¶
(a) Modes 1 and 2 (109 Hz)
(b) Modes 3 and 4 (570 Hz)
(c) Mode 5 (615 Hz)
Figure 9.4.6 EX09 Cylindrical Shell Mode Shapes
EX10A Wine Glass¶
 |  |  |
| (a) Mode 1 (101 Hz) | (b) Mode 2 (102 Hz) | (c) Mode 3 (354 Hz) |
 |  | |
| (d) Mode 4 (1335 Hz) | (e) Mode 5 (1336 Hz) |
Figure 9.4.7 EX10A Wine Glass Mode Shapes