# 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 language English 1029-1041 13 Mechanical Systems and Signal Processing 116 1 Aug 2018 https://doi.org/10.1016/j.ymssp.2018.07.008 Published - 1 Feb 2019 Yes

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

### Cite this

@article{8f142316fa994c709aeca9fdbd9a3dec,
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",
year = "2019",
month = "2",
day = "1",
doi = "10.1016/j.ymssp.2018.07.008",
language = "English",
volume = "116",
pages = "1029--1041",
journal = "Mechanical Systems and Signal Processing",
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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

Y1 - 2019/2/1

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.

KW - Amplitude-frequency response

KW - Cubic nonlinearity

KW - Dynamical system

KW - Polynomial dimensional decomposition

KW - Rotor system

KW - Uncertainty

UR - http://www.scopus.com/inward/record.url?scp=85050825057&partnerID=8YFLogxK

U2 - 10.1016/j.ymssp.2018.07.008

DO - 10.1016/j.ymssp.2018.07.008

M3 - Article

AN - SCOPUS:85050825057

VL - 116

SP - 1029

EP - 1041

JO - Mechanical Systems and Signal Processing

JF - Mechanical Systems and Signal Processing

SN - 0888-3270

ER -