N. Wu, Kuan Lu, Yulin Jin, Haopeng Zhang, Yushu Chen
{"title":"The Applications of Order Reduction Methods in Nonlinear Dynamic Systems","authors":"N. Wu, Kuan Lu, Yulin Jin, Haopeng Zhang, Yushu Chen","doi":"10.32604/sv.2020.09783","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":49496,"journal":{"name":"Sound and Vibration","volume":"272 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Sound and Vibration","FirstCategoryId":"1089","ListUrlMain":"https://doi.org/10.32604/sv.2020.09783","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"ACOUSTICS","Score":null,"Total":0}
引用次数: 0
Abstract
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.
期刊介绍:
Sound & Vibration is a journal intended for individuals with broad-based interests in noise and vibration, dynamic measurements, structural analysis, computer-aided engineering, machinery reliability, and dynamic testing. The journal strives to publish referred papers reflecting the interests of research and practical engineering on any aspects of sound and vibration. Of particular interest are papers that report analytical, numerical and experimental methods of more relevance to practical applications.
Papers are sought that contribute to the following general topics:
-broad-based interests in noise and vibration-
dynamic measurements-
structural analysis-
computer-aided engineering-
machinery reliability-
dynamic testing