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For the pressure amplitudes in Cases 1 and 3, similar to Case 2, it can be seen from Figures 35(a) and 37(a) that the predictions by the elastic models are not in good agreement with the experimental data, in which the amplitudes by the CB-UF are closest to the experimental; for Case 1, the first four order amplitudes by the CB-UF are 0.96, 0.24, 0.13 and 0.08 m, respectively, but the first four order amplitudes obtained from the experimental are 0.33, 0.07, 0.03 and 0.02 m, respectively; for Case 3, the first four order amplitudes by the CB-UF are 12.77, 3.19, 1.71 and 1.01 m, respectively, but the first four order amplitudes obtained from the experimental are 5.82, 1.20, 0.55 and 0.31 m, respectively. Figures 36(a) and 38(a) show that the amplitudes predicted by the viscoelastic models are generally in good agreement with the experimental compared to those by the elastic models. As can be seen in Table 6, the amplitudes predicted by the CB-UF-VE are closest to the experimental for Case 1. Also, the relative errors by the three viscoelastic models for Case 3 are shown in Table 9.
Table 6

Relative errors of the first four order pressure amplitudes in the frequency domain at T1 by the three viscoelastic models for Case 1

OrderRelative errors by the viscoelastic models (–)
SF-VE (%)CB-UF-VE (%)MIAB-UF-VE (%)
32.90 5.01 5.86 
26.72 1.57 15.97 
20.05 1.66 11.35 
8.88 1.95 2.49 
OrderRelative errors by the viscoelastic models (–)
SF-VE (%)CB-UF-VE (%)MIAB-UF-VE (%)
32.90 5.01 5.86 
26.72 1.57 15.97 
20.05 1.66 11.35 
8.88 1.95 2.49 
Table 7

First 11 order harmonic frequencies of transient pressure at T1 by the elastic models and the experimental data for Case 1

OrderPredicted frequencies and experimental data (Hz)
FrictionlessSFCB-UFMIAB-UFExperimental data
0.35 0.35 0.35 0.35 0.35 
1.10 1.10 1.10 1.10 1.00 
1.80 1.80 1.80 1.80 1.75 
2.55 2.55 2.55 2.50 2.40 
3.30 3.30 3.25 3.20 3.10 
4.00 4.00 4.00 3.95 3.90 
4.75 4.75 4.75 4.65 4.60 
5.45 5.45 5.45 5.40 5.30 
6.20 6.20 6.20 6.10 6.10 
10 6.90 6.90 6.90 6.80 6.50 
11 7.65 7.65 7.65 7.50 6.80 
OrderPredicted frequencies and experimental data (Hz)
FrictionlessSFCB-UFMIAB-UFExperimental data
0.35 0.35 0.35 0.35 0.35 
1.10 1.10 1.10 1.10 1.00 
1.80 1.80 1.80 1.80 1.75 
2.55 2.55 2.55 2.50 2.40 
3.30 3.30 3.25 3.20 3.10 
4.00 4.00 4.00 3.95 3.90 
4.75 4.75 4.75 4.65 4.60 
5.45 5.45 5.45 5.40 5.30 
6.20 6.20 6.20 6.10 6.10 
10 6.90 6.90 6.90 6.80 6.50 
11 7.65 7.65 7.65 7.50 6.80 
Figure 35

(a) Pressure head amplitudes at T1 for Case 1 (V0 = 0.0278 m/s) in the frequency domain produced by different elastic models and the experimental data. (b) Corresponding first 11 harmonic frequencies.

Figure 35

(a) Pressure head amplitudes at T1 for Case 1 (V0 = 0.0278 m/s) in the frequency domain produced by different elastic models and the experimental data. (b) Corresponding first 11 harmonic frequencies.

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Figure 36

(a) Pressure head amplitudes at T1 for Case 1 (V0 = 0.0278 m/s) in the frequency domain produced by different viscoelastic models and the experimental data. (b) Corresponding first four harmonic frequencies.

Figure 36

(a) Pressure head amplitudes at T1 for Case 1 (V0 = 0.0278 m/s) in the frequency domain produced by different viscoelastic models and the experimental data. (b) Corresponding first four harmonic frequencies.

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Figure 37

(a) Pressure head amplitudes at T1 for Case 3 (V0 = 0.9946 m/s) in the frequency domain produced by different elastic models and the experimental data. (b) Corresponding first 11 harmonic frequencies.

Figure 37

(a) Pressure head amplitudes at T1 for Case 3 (V0 = 0.9946 m/s) in the frequency domain produced by different elastic models and the experimental data. (b) Corresponding first 11 harmonic frequencies.

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Figure 38

(a) Pressure head amplitudes at T1 for Case 3 (V0 = 0.9946 m/s) in the frequency domain produced by different viscoelastic models and the experimental data. (b) Corresponding first four harmonic frequencies.

Figure 38

(a) Pressure head amplitudes at T1 for Case 3 (V0 = 0.9946 m/s) in the frequency domain produced by different viscoelastic models and the experimental data. (b) Corresponding first four harmonic frequencies.

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