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Example of Actual Model for Eigenvalue Analysis

Actual Model Examples for Eigenvalue Analysis

Analysis model

A list of examples of the actual verification models for eigenvalue analysis is presented in Table 9.3.1. The model shapes of EX07 (turbine rotor) and EX08 (spring) are also shown in Figs. 9.3.1 and 9.3.2. The other model shapes are the same as those of the examples previously discussed in the elastic static analysis, which has the same verification content. The examples of the element types 731 and 741 require a separate direct method solver.

Table 9.3.1: Examples of actual model verification for eigenvalue analysis
Case Name Element Type Verification Model No. of Nodes No. of 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 (midium) 48,803 292,818

Turbine rotor (EX07)

Fig. 9.3.1: Turbine rotor (EX07)

Spring (EX08)

Fig. 9.3.2: Spring (EX08)

Analysis Results

The vibration mode and natural frequency are shown in the following.

(1) EX06 Turbine blade

(a) Mode 1 (1170 kHz) (b) Mode 2(3250kHz)
(a) Mode 1 (1170 kHz) (b) Mode 2(3250kHz)
(c) Mode 3(4130kHz) (d) Mode 4(4140kHz)
(c) Mode 3(4130kHz) (d) Mode 4(4140kHz)
(e) Mode 5(8210kHz)
(e) Mode 5(8210kHz)
Fig. 9.3.3: EX06, turbine blade vibration mode

(2) EX07 Turbine rotor

(a) Mode 1(1067Hz) (b) Mode 2(1072Hz)
(a) Mode 1(1067Hz) (b) Mode 2(1072Hz)
(c) Mode 3(1072Hz) (d) Mode 4(1093Hz)
(c) Mode 3(1072Hz) (d) Mode 4(1093Hz)
(e) Mode 5(1093Hz)
(e) Mode 5(1093Hz)
Fig. 9.3.4: EX07, Turbine rotor vibration mode

EX08 Spring

Mode 1 (445Hz) Mode 2 (446Hz) Mode 3 (908Hz)
Mode 1 (445Hz) Mode 2 (446Hz) Mode 3 (908Hz)
Mode 4 (985Hz) Mode 5 (1819Hz)
Mode 4 (985Hz) Mode 5 (1819Hz)
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
Fig. 9.3.5: EX08, spring vibration mode

(4) EX09 Cylindrical shell

(a) Mode 1, 2 (109 Hz)

(a) Mode 1, 2 (109 Hz)

(b) Mode 3,4(570Hz)

(b) Mode 3,4(570Hz)

c) Mode 5(615Hz)

(c) Mode 5(615Hz)

Fig. 9.3.6: EX09, cylindrical shell vibration mode

EX10A Wine glass

(a) Mode 1(101Hz) (b) Mode 2(102Hz) (c) Mode 3(354Hz)
(a) Mode 1(101Hz) (b) Mode 2(102Hz) (c) Mode 3(354Hz)
(d) Mode 4(1335Hz) (e) Mode 5(1336Hz)
(d) Mode 4(1335Hz) (e) Mode 5(1336Hz)
Fig. 9.3.7: EX10A Wine Glass Vibration Mode