The first 11 order harmonic frequencies by the elastic models and obtained from the experimental for Case 1 in Figure 35(b) and for Case 3 in Figure 37(b) are shown in Tables 7 and 10, respectively. The harmonic frequencies by the frictionless elastic model and the SF are, respectively, equal, and except that the predicted fundamental frequency is equal to the experimental, there are some differences between the other harmonic frequencies and the corresponding experimental data; for Case 1, the relative error of the ninth harmonic frequency is the smallest (1.64%), and the relative error of the 11th harmonic frequency is the largest (12.5%); for Case 3, the relative error of the third  harmonic frequency is the smallest (3.85%) and the relative error of the 11th harmonic frequency is the largest (15%). For Case 1, except that there is a certain difference between the fifth harmonic frequency (3.25 Hz) by the CB-UF and that by the frictionless elastic model (3.3 Hz), the other frequencies by the CB-UF are the same as those by the frictionless elastic model correspondingly; except that the fundamental frequency by the CB-UF is the same as the experimental, there are some differences between the other order frequencies and the corresponding experimental data, the smallest relative error is 1.64% (the ninth frequency) and the largest relative error is 12.5% (the 11th frequency). For Case 3, except that there is a certain difference between the 11th harmonic frequency (7.60 Hz) by the CB-UF and that (7.67 Hz) by the frictionless elastic model, the other harmonic frequencies by the CB-UF are the same as the corresponding harmonic frequencies by the frictionless elastic model; except that the fundamental frequency by the CB-UF is equal to the experimental, there are some differences between other frequencies by the CB-UF and the corresponding experimental data, the smallest relative error of the seventh  harmonic frequency is 2.13% and the largest relative error of the 11th harmonic frequency is 14%. For Case 1, the fundamental frequency and the ninth harmonic frequency by the MIAB-UF are the same as the corresponding experimental data, but there are some differences between the other frequencies and the corresponding experimental data, among which the relative error of the seventh  frequency is the smallest (1.09%), and the relative error of the 11th frequency is the largest (10.29%). For Case 3, the fundamental frequency by the MIAB-UF is the same as the experimental, but there are some differences between other harmonic frequencies and the corresponding experimental data, the smallest relative error of the seventh  harmonic frequency is 1.09%, and the largest relative error of the 11th harmonic frequency is 13%. On the whole, similar to Case 2, the frequencies predicted by the elastic models are not in good agreement with the experimental.

Table 8

First four order harmonic frequencies of transient pressure at T1 by the viscoelastic models and the experimental data for Case 1

OrderPredicted frequencies and experimental data (Hz)
SF-VECB-UF-VEMIAB-UF-VEExperimental data
0.35 0.35 0.35 0.35
1.10 1.10 1.10 1.00
1.80 1.80 1.80 1.75
2.55 2.55 2.50 2.40
OrderPredicted frequencies and experimental data (Hz)
SF-VECB-UF-VEMIAB-UF-VEExperimental data
0.35 0.35 0.35 0.35
1.10 1.10 1.10 1.00
1.80 1.80 1.80 1.75
2.55 2.55 2.50 2.40
Table 9

Relative errors of the first four order pressure amplitudes in the frequency domain at T1 by the three viscoelastic models for Case 3

OrderRelative errors by the viscoelastic models (–)
SF-VE (%)CB-UF-VE (%)MIAB-UF-VE (%)
2.53 8.17 6.10
5.07 6.88 3.35
13.07 0.71 2.14
3.55 8.91 0.48
OrderRelative errors by the viscoelastic models (–)
SF-VE (%)CB-UF-VE (%)MIAB-UF-VE (%)
2.53 8.17 6.10
5.07 6.88 3.35
13.07 0.71 2.14
3.55 8.91 0.48

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