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Transient solution of stochastic oscillators with both odd and even nonlinearity under modulated Gaussian white noise
Luo, Jie; Er, Guo-Kang; Iu, Vai Pan; Lam, Chi Chiu
2023-08-08
Source PublicationPhysical Review E
ISSN2470-0053
Volume108Issue:2Pages:024209
Abstract

This study presents an improved solution procedure for determining the transient probability density function (PDF) solutions of the nonlinear oscillators with both odd and even nonlinearity under modulated random stimulation, which is an extension of the exponential-polynomial-closure approach. An evolutionary exponentialpolynomial function with time-varying undetermined variables is considered as the transient probabilistic solution. By selecting a set of independent evolutionary base functions spanning a Rn space as weight functions, a set of ordinary differential equations can be formulated by integrating the weighted residual error. The undetermined variables can be determined numerically by solving those ordinary differential equations. Three numerical examples illustrate that the improved solution procedure can acquire the transient probabilistic responses of the stochastic dynamic systems effectively and efficiently even in the PDF solution tails when compared with Monte Carlo simulation. Moreover, the results indicate that the PDF solutions of the oscillators are asymmetrical at their nonzero means due to the influence of even nonlinearity. The nonstationary behaviors of the system responses are also investigated along with the behavior of modulated Gaussian white noise.

DOI10.1103/PhysRevE.108.024209
URLView the original
Indexed BySCIE
Funding ProjectApplications and investigation of artificial neural network in analyzing the static and dynamic structures
WOS Research AreaPhysics
WOS SubjectPhysics, Fluids & Plasmas ; Physics, Mathematical
WOS IDWOS:001053111700004
PublisherAmerican Physics Society
Scopus ID2-s2.0-85167972128
Fulltext Access
Citation statistics
Document TypeJournal article
CollectionDEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING
Faculty of Science and Technology
Corresponding AuthorLuo, Jie
AffiliationUniversity of Macau
First Author AffilicationUniversity of Macau
Corresponding Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Luo, Jie,Er, Guo-Kang,Iu, Vai Pan,et al. Transient solution of stochastic oscillators with both odd and even nonlinearity under modulated Gaussian white noise[J]. Physical Review E, 2023, 108(2), 024209.
APA Luo, Jie., Er, Guo-Kang., Iu, Vai Pan., & Lam, Chi Chiu (2023). Transient solution of stochastic oscillators with both odd and even nonlinearity under modulated Gaussian white noise. Physical Review E, 108(2), 024209.
MLA Luo, Jie,et al."Transient solution of stochastic oscillators with both odd and even nonlinearity under modulated Gaussian white noise".Physical Review E 108.2(2023):024209.
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