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Analytical Modeling and Data-Driven Uncertainty Analysis of the Vibration Response of Partially Liquid-Filled Rotors Under Lateral Excitation.

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Title: Analytical Modeling and Data-Driven Uncertainty Analysis of the Vibration Response of Partially Liquid-Filled Rotors Under Lateral Excitation.
Authors: Sun, Hongyun1 (AUTHOR) shy5006@sylu.edu.cn, Bai, Xinjie1,2 (AUTHOR), Li, Xinqi1 (AUTHOR), Zhang, Hongyuan1,2 (AUTHOR), Shao, Yang1 (AUTHOR), Yuan, Huiqun2 (AUTHOR)
Source: Materials (1996-1944). May2026, Vol. 19 Issue 9, p1728. 28p.
Subjects: Fluid-structure interaction, Rotors, Artificial neural networks, Mathematical models, Statistical models, Vibration (Mechanics), Mechanical vibration research, Uncertainty (Information theory)
Abstract: Partially liquid-filled rotor systems subjected to lateral excitation exhibit pronounced fluid–structure interaction, leading to complex and highly sensitive vibration responses. To enable efficient probabilistic prediction under parametric uncertainty, this study develops a deterministic–data-driven framework for a rigid hollow rotor partially filled with liquid. Based on small-perturbation flow theory, the liquid-induced feedback forces are analytically derived and incorporated into the coupled rotor–liquid dynamic equations, yielding a closed-form steady-state solution. The results reveal that lateral excitation in one direction induces coupled vibration in the orthogonal direction, resulting in an elliptical whirl trajectory of the rotor center. The vibration characteristics depend jointly on excitation frequency and rotor angular velocity, and for a given angular velocity, two critical excitation frequencies are identified at which the response amplitude increases sharply. Surrogate models based on a backpropagation neural network (BPNN) and a support vector machine (SVM) are constructed and validated, with the BPNN demonstrating superior predictive accuracy. Uncertainty analysis further shows that the maximum vibration amplitude exhibits asymmetric, non-Gaussian distributions even under normally distributed inputs, and excessive amplification may occur beyond certain uncertainty levels. The proposed framework provides a robust tool for probabilistic vibration assessment and uncertainty-informed design of partially liquid-filled rotor systems. [ABSTRACT FROM AUTHOR]
Copyright of Materials (1996-1944) is the property of MDPI and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Analytical Modeling and Data-Driven Uncertainty Analysis of the Vibration Response of Partially Liquid-Filled Rotors Under Lateral Excitation.
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  Data: <searchLink fieldCode="AR" term="%22Sun%2C+Hongyun%22">Sun, Hongyun</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> shy5006@sylu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Bai%2C+Xinjie%22">Bai, Xinjie</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Li%2C+Xinqi%22">Li, Xinqi</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Zhang%2C+Hongyuan%22">Zhang, Hongyuan</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Shao%2C+Yang%22">Shao, Yang</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Yuan%2C+Huiqun%22">Yuan, Huiqun</searchLink><relatesTo>2</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Materials+%281996-1944%29%22">Materials (1996-1944)</searchLink>. May2026, Vol. 19 Issue 9, p1728. 28p.
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  Data: <searchLink fieldCode="DE" term="%22Fluid-structure+interaction%22">Fluid-structure interaction</searchLink><br /><searchLink fieldCode="DE" term="%22Rotors%22">Rotors</searchLink><br /><searchLink fieldCode="DE" term="%22Artificial+neural+networks%22">Artificial neural networks</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+models%22">Mathematical models</searchLink><br /><searchLink fieldCode="DE" term="%22Statistical+models%22">Statistical models</searchLink><br /><searchLink fieldCode="DE" term="%22Vibration+%28Mechanics%29%22">Vibration (Mechanics)</searchLink><br /><searchLink fieldCode="DE" term="%22Mechanical+vibration+research%22">Mechanical vibration research</searchLink><br /><searchLink fieldCode="DE" term="%22Uncertainty+%28Information+theory%29%22">Uncertainty (Information theory)</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Partially liquid-filled rotor systems subjected to lateral excitation exhibit pronounced fluid–structure interaction, leading to complex and highly sensitive vibration responses. To enable efficient probabilistic prediction under parametric uncertainty, this study develops a deterministic–data-driven framework for a rigid hollow rotor partially filled with liquid. Based on small-perturbation flow theory, the liquid-induced feedback forces are analytically derived and incorporated into the coupled rotor–liquid dynamic equations, yielding a closed-form steady-state solution. The results reveal that lateral excitation in one direction induces coupled vibration in the orthogonal direction, resulting in an elliptical whirl trajectory of the rotor center. The vibration characteristics depend jointly on excitation frequency and rotor angular velocity, and for a given angular velocity, two critical excitation frequencies are identified at which the response amplitude increases sharply. Surrogate models based on a backpropagation neural network (BPNN) and a support vector machine (SVM) are constructed and validated, with the BPNN demonstrating superior predictive accuracy. Uncertainty analysis further shows that the maximum vibration amplitude exhibits asymmetric, non-Gaussian distributions even under normally distributed inputs, and excessive amplification may occur beyond certain uncertainty levels. The proposed framework provides a robust tool for probabilistic vibration assessment and uncertainty-informed design of partially liquid-filled rotor systems. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Materials (1996-1944) is the property of MDPI and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.3390/ma19091728
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      – Code: eng
        Text: English
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        PageCount: 28
        StartPage: 1728
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      – SubjectFull: Fluid-structure interaction
        Type: general
      – SubjectFull: Rotors
        Type: general
      – SubjectFull: Artificial neural networks
        Type: general
      – SubjectFull: Mathematical models
        Type: general
      – SubjectFull: Statistical models
        Type: general
      – SubjectFull: Vibration (Mechanics)
        Type: general
      – SubjectFull: Mechanical vibration research
        Type: general
      – SubjectFull: Uncertainty (Information theory)
        Type: general
    Titles:
      – TitleFull: Analytical Modeling and Data-Driven Uncertainty Analysis of the Vibration Response of Partially Liquid-Filled Rotors Under Lateral Excitation.
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          Name:
            NameFull: Sun, Hongyun
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            NameFull: Bai, Xinjie
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            NameFull: Li, Xinqi
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            NameFull: Zhang, Hongyuan
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            – D: 01
              M: 05
              Text: May2026
              Type: published
              Y: 2026
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              Value: 19
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              Value: 9
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            – TitleFull: Materials (1996-1944)
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