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Real-Model Examples for Modal Analysis¶
Analysis Models¶
Table 9.3.1 lists the real-model verification examples for modal analysis. Among these, the model geometries for EX07 (turbine rotor) and EX08 (spring) are shown in Figures 9.3.1 and 9.3.2. The other model geometries are the same as those of the verification examples for elastic static analysis with corresponding verification content and have already been shown. Note that a separate direct solver is required to run the examples for element types 731 and 741.
Table 9.3.1 Real-model verification examples for modal analysis
| Case Name | Element Type | Verification Model | Number of Nodes | Number of DOFs |
|---|---|---|---|---|
| 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 (midium) | 48,803 | 292,818 |
Figure 9.3.1 Turbine rotor (EX07)
Figure 9.3.2 Spring (EX08)
Analysis Results¶
The mode shapes and natural frequencies are shown below.
EX06 Turbine Blade¶
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| (a) Mode 1 (1170 kHz) | (b) Mode 2(3250kHz) |
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| (c) Mode 3(4130kHz) | (d) Mode 4(4140kHz) |
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| (e) Mode 5(8210kHz) |
Figure 9.3.3 EX06 Turbine Blade Mode Shapes
EX07 Turbine Rotor¶
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| (a) Mode 1(1067Hz) | (b) Mode 2(1072Hz) |
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| (c) Mode 3(1072Hz) | (d) Mode 4(1093Hz) |
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| (e) Mode 5(1093Hz) | |
Figure 9.3.4 EX07 Turbine Rotor Mode Shapes
EX08 Spring¶
| Mode 1 (445Hz) | Mode 2 (446Hz) | Mode 3 (908Hz) |
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| Mode 4 (985Hz) | Mode 5 (1819Hz) | |
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| 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 9.3.5 EX08 Spring Mode Shapes
EX09 Cylindrical Shell¶
(a) Mode 1, 2 (109 Hz)
(b) Mode 3,4(570Hz)
(c) Mode 5(615Hz)
Figure 9.3.6 EX09 Cylindrical Shell Mode Shapes
EX10A Wine Glass¶
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| (a) Mode 1(101Hz) | (b) Mode 2(102Hz) | (c) Mode 3(354Hz) |
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| (d) Mode 4(1335Hz) | (e) Mode 5(1336Hz) |
Figure 9.3.7 EX10A Wine Glass Mode Shapes