Statistical moment analysis of nonlinear rotor system with multi uncertain variables

Kuan Lu, Yongfeng Yang, Yebao Xia, Chao Fu

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

The statistical moments of the dynamical system models with uncertainties are analyzed in this paper. The analytical and numerical cases of the polynomial dimensional decomposition to solve the dynamical responses are provided. First, the polynomial dimensional decomposition method is applied to study a two-degree-of-freedom spring system model with stiffness uncertainty. Second, a linear rotor system model with eight random variables is discussed in the cases of different polynomial orders. Third, a rotor system model supported by cubically nonlinear stiffness is established by the Newton's second law. The amplitude-frequency responses of nine and twelve uncertain variables are calculated by combining the harmonic balance method and the polynomial dimensional decomposition method. The accuracy of the polynomial dimensional decomposition method is verified via comparing with the Monte Carlo Simulation method. The applications of the polynomial dimensional decomposition method in the nonlinear rotor systems can provide theoretical guidance to study complex rotor-bearing systems in the future.

Original languageEnglish
Pages (from-to)1029-1041
Number of pages13
JournalMechanical Systems and Signal Processing
Volume116
Early online date1 Aug 2018
DOIs
Publication statusPublished - 1 Feb 2019
Externally publishedYes

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Rotors
Polynomials
Decomposition
Bearings (structural)
Stiffness
Degrees of freedom (mechanics)
Random variables
Frequency response
Dynamical systems
Uncertainty

Cite this

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title = "Statistical moment analysis of nonlinear rotor system with multi uncertain variables",
abstract = "The statistical moments of the dynamical system models with uncertainties are analyzed in this paper. The analytical and numerical cases of the polynomial dimensional decomposition to solve the dynamical responses are provided. First, the polynomial dimensional decomposition method is applied to study a two-degree-of-freedom spring system model with stiffness uncertainty. Second, a linear rotor system model with eight random variables is discussed in the cases of different polynomial orders. Third, a rotor system model supported by cubically nonlinear stiffness is established by the Newton's second law. The amplitude-frequency responses of nine and twelve uncertain variables are calculated by combining the harmonic balance method and the polynomial dimensional decomposition method. The accuracy of the polynomial dimensional decomposition method is verified via comparing with the Monte Carlo Simulation method. The applications of the polynomial dimensional decomposition method in the nonlinear rotor systems can provide theoretical guidance to study complex rotor-bearing systems in the future.",
keywords = "Amplitude-frequency response, Cubic nonlinearity, Dynamical system, Polynomial dimensional decomposition, Rotor system, Uncertainty",
author = "Kuan Lu and Yongfeng Yang and Yebao Xia and Chao Fu",
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Statistical moment analysis of nonlinear rotor system with multi uncertain variables. / Lu, Kuan; Yang, Yongfeng; Xia, Yebao; Fu, Chao.

In: Mechanical Systems and Signal Processing, Vol. 116, 01.02.2019, p. 1029-1041.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Statistical moment analysis of nonlinear rotor system with multi uncertain variables

AU - Lu, Kuan

AU - Yang, Yongfeng

AU - Xia, Yebao

AU - Fu, Chao

PY - 2019/2/1

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N2 - The statistical moments of the dynamical system models with uncertainties are analyzed in this paper. The analytical and numerical cases of the polynomial dimensional decomposition to solve the dynamical responses are provided. First, the polynomial dimensional decomposition method is applied to study a two-degree-of-freedom spring system model with stiffness uncertainty. Second, a linear rotor system model with eight random variables is discussed in the cases of different polynomial orders. Third, a rotor system model supported by cubically nonlinear stiffness is established by the Newton's second law. The amplitude-frequency responses of nine and twelve uncertain variables are calculated by combining the harmonic balance method and the polynomial dimensional decomposition method. The accuracy of the polynomial dimensional decomposition method is verified via comparing with the Monte Carlo Simulation method. The applications of the polynomial dimensional decomposition method in the nonlinear rotor systems can provide theoretical guidance to study complex rotor-bearing systems in the future.

AB - The statistical moments of the dynamical system models with uncertainties are analyzed in this paper. The analytical and numerical cases of the polynomial dimensional decomposition to solve the dynamical responses are provided. First, the polynomial dimensional decomposition method is applied to study a two-degree-of-freedom spring system model with stiffness uncertainty. Second, a linear rotor system model with eight random variables is discussed in the cases of different polynomial orders. Third, a rotor system model supported by cubically nonlinear stiffness is established by the Newton's second law. The amplitude-frequency responses of nine and twelve uncertain variables are calculated by combining the harmonic balance method and the polynomial dimensional decomposition method. The accuracy of the polynomial dimensional decomposition method is verified via comparing with the Monte Carlo Simulation method. The applications of the polynomial dimensional decomposition method in the nonlinear rotor systems can provide theoretical guidance to study complex rotor-bearing systems in the future.

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KW - Dynamical system

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