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

Order . | Predicted frequencies and experimental data (Hz) . | |||
---|---|---|---|---|

SF-VE . | CB-UF-VE . | MIAB-UF-VE . | Experimental data . | |

1 | 0.35 | 0.35 | 0.35 | 0.35 |

2 | 1.10 | 1.10 | 1.10 | 1.00 |

3 | 1.80 | 1.80 | 1.80 | 1.75 |

4 | 2.55 | 2.55 | 2.50 | 2.40 |

Order . | Predicted frequencies and experimental data (Hz) . | |||
---|---|---|---|---|

SF-VE . | CB-UF-VE . | MIAB-UF-VE . | Experimental data . | |

1 | 0.35 | 0.35 | 0.35 | 0.35 |

2 | 1.10 | 1.10 | 1.10 | 1.00 |

3 | 1.80 | 1.80 | 1.80 | 1.75 |

4 | 2.55 | 2.55 | 2.50 | 2.40 |

Table 9

Order . | Relative errors by the viscoelastic models (–) . | ||
---|---|---|---|

SF-VE (%) . | CB-UF-VE (%) . | MIAB-UF-VE (%) . | |

1 | 2.53 | 8.17 | 6.10 |

2 | 5.07 | 6.88 | 3.35 |

3 | 13.07 | 0.71 | 2.14 |

4 | 3.55 | 8.91 | 0.48 |

Order . | Relative errors by the viscoelastic models (–) . | ||
---|---|---|---|

SF-VE (%) . | CB-UF-VE (%) . | MIAB-UF-VE (%) . | |

1 | 2.53 | 8.17 | 6.10 |

2 | 5.07 | 6.88 | 3.35 |

3 | 13.07 | 0.71 | 2.14 |

4 | 3.55 | 8.91 | 0.48 |

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