Vibration Analysis of Rotors Under Uncertainty Based on Legendre Series

  • Chao Fu
  • Xingmin Ren
  • Yongfeng YangEmail author
Original Paper



In rotor systems, uncertainty can arise in occasions such as manufacture errors and variations in geometry during lifetime. In the presence of uncertainty, the deterministic analysis procedures often fail to give a reasonable estimate of the rotordynamics. This paper employs an interval procedure to quantify effects of bounded uncertainty on variations of the vibration responses.


A derivative-based Legendre interval method is applied to the uncertainty quantification of rotor systems. It works non-intrusively and can deal with each uncertain parameter individually. The roots of Legendre polynomials are used as collocations and sample responses of the rotor are obtained using the Gauss–Legendre quadrature.


On the basis of the method developed, the vibration characteristics of a rotor under several uncertain parameters are presented. Comparative vibration amplitudes are illustrated by the interval method and the Monte Carlo simulation.


The interval method is verified to possess good numerical performance. Results show that uncertain parameters will significantly influence the vibration behaviors. Unlike the deterministic model, the response is no longer a certain value for a specified speed but a response range which is defined by lower and upper bound. Furthermore, the resonance range is expanded and peak shift is spotted.


Uncertainty Rotor system Legendre series 



This work was supported by Aerospace Science, Technology Innovation Fund under Grant No. 2016KC060013 and NPU Aoxiang New Star.


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© KrishteleMaging Solutions Private Limited 2018

Authors and Affiliations

  1. 1.Institute of Vibration EngineeringNorthwestern Polytechnical UniversityXi’anPeople’s Republic of China

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