Nonlinear Dynamics

, Volume 93, Issue 4, pp 2003–2018 | Cite as

Statistical moment analysis of multi-degree of freedom dynamic system based on polynomial dimensional decomposition method

Original Paper


The first two moments of the steady-state response of the spring and rotor models are determined by the polynomial dimensional decomposition (PDD) method and the Monte Carlo simulation (MCS) method in this paper. Both the analytical and numerical cases of the PDD method in the dynamical models are provided, and the response of the numerical case is calculated via the harmonic balance and PDD methods. The PDD can describe the amplitude–frequency characteristics of the dynamical models with random variables except the frequencies around the resonant frequencies. These results are shown as a three-DOF spring model with stiffness uncertainty, rotor models with four and nine random variables and nonlinear rotor model with thirteen random variables, respectively. The effects of larger uncertainties and polynomial order are also highlighted. The efficiency of the PDD method is verified via comparing with the MCS method. The applications of the PDD method to the rotor model can provide guidance to further study the rotor systems supported by bearings.


Polynomial dimensional decomposition Monte Carlo simulation Statistical moments Harmonic balance Uncertainty Rotor system 



I appreciate the support of the China Scholarship Council and the guidance of professor Sharif Rahman in the university of Iowa.

Compliance with ethical standards

Conflict of interest

There is no conflict of interest between the authors.


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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Vibration EngineeringNorthwestern Polytechnical UniversityXi’anPeople’s Republic of China
  2. 2.College of EngineeringThe University of IowaIowa CityUSA

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