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

Fig. 9.3.1: Turbine rotor (EX07)

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)
(c) Mode 3(4130kHz)	(d) Mode 4(4140kHz)
(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)
(c) Mode 3(1072Hz)	(d) Mode 4(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 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)

(b) Mode 3,4(570Hz)

(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)
(d) Mode 4(1335Hz)	(e) Mode 5(1336Hz)

Fig. 9.3.7: EX10A Wine Glass Vibration Mode