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The Applications of Order Reduction Methods in Nonlinear Dynamic Systems

Nan Wu1,#, Kuan Lu1,2,#,*, Yulin Jin2,3,*, Haopeng Zhang1, Yushu Chen2

1 Institute of Vibration Engineering, Northwestern Polytechnical University, Xi’an, 710072, China
2 School of Astronautics, Harbin Institute of Technology, Harbin, 150001, China
3 School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu, 611731, China
# Co-first Authors: Nan Wu and Kuan Lu

* Corresponding Authors: Kuan Lu. Email: ; Yulin Jin. Email:

Sound & Vibration 2020, 54(2), 113-125.


Two different order reduction methods of the deterministic and stochastic systems are discussed in this paper. First, the transient proper orthogonal decomposition (T-POD) method is introduced based on the high-dimensional nonlinear dynamic system. The optimal order reduction conditions of the T-POD method are provided by analyzing the rotor-bearing system with pedestal looseness fault at both ends. The efficiency of the T-POD method is verified via comparing with the results of the original system. Second, the polynomial dimensional decomposition (PDD) method is applied to the 2 DOFs spring system considering the uncertain stiffness to study the amplitude-frequency response. The numerical results obtained by the PDD method agree well with the Monte Carlo simulation (MCS) method. The results of the PDD method can approximate to MCS better with the increasing of the polynomial order. Meanwhile, the Uniform-Legendre polynomials can eliminate perturbation of the PDD method to a certain extent via comparing it with the Gaussian-Hermite polynomials.


Cite This Article

Wu, N., Lu, K., Jin, Y., Zhang, H., Chen, Y. (2020). The Applications of Order Reduction Methods in Nonlinear Dynamic Systems. Sound & Vibration, 54(2), 113–125.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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