For Case 1, it can be seen from Figure 36(b) and Table 8 that the first four harmonic frequencies by the SF-VE and the CB-UF-VE are, respectively, equal, the first and third harmonic frequencies are the same as the corresponding experimental data, but the second and fourth harmonic frequencies are larger than the corresponding experimental, and the relative errors are 5 and 2.08%, respectively. Except for the third harmonic frequency (relative error 2.86%) by the MIAB-UF-VE, the other harmonic frequencies are equal to the corresponding experimental data. In general, the harmonic frequencies predicted by the viscoelastic models are in good agreement with the experimental, in which the predictions by the MIAB-UF-VE are most accurate, and those by the SF-VE and the CB-UF-VE have the same accuracy.

Table 10

First 11 order harmonic frequencies of transient pressure at T1 by the elastic models and the experimental data for Case 3

OrderPredicted frequencies and experimental data (Hz)
FrictionlessSFCB-UFMIAB-UFExperimental Data
0.33 0.33 0.33 0.33 0.33
1.07 1.07 1.07 1.07 1.00
1.80 1.80 1.80 1.80 1.73
2.53 2.53 2.53 2.53 2.40
3.27 3.27 3.27 3.20 3.13
4.00 4.00 4.00 3.93 3.80
4.73 4.73 4.73 4.67 4.53
5.47 5.47 5.47 5.33 5.13
6.20 6.20 6.20 6.13 5.73
10 6.93 6.93 6.93 6.80 6.27
11 7.67 7.67 7.60 7.53 6.67
OrderPredicted frequencies and experimental data (Hz)
FrictionlessSFCB-UFMIAB-UFExperimental Data
0.33 0.33 0.33 0.33 0.33
1.07 1.07 1.07 1.07 1.00
1.80 1.80 1.80 1.80 1.73
2.53 2.53 2.53 2.53 2.40
3.27 3.27 3.27 3.20 3.13
4.00 4.00 4.00 3.93 3.80
4.73 4.73 4.73 4.67 4.53
5.47 5.47 5.47 5.33 5.13
6.20 6.20 6.20 6.13 5.73
10 6.93 6.93 6.93 6.80 6.27
11 7.67 7.67 7.60 7.53 6.67

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