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Parameter-splitting perturbation method for the improved solutions to strongly nonlinear systems
Du,Hai En; Er,Guo Kang; Iu,Vai Pan
2019
Source PublicationNonlinear Dynamics
ISSN1573-269X
Volume96Pages:1847-1863
Abstract

A procedure named parameter-splitting perturbation method for improving the perturbation solutions to the forced vibrations of strongly nonlinear oscillators is proposed. The idea of the proposed procedure is presented in general first. After that, it is applied to optimize the solutions obtained by the multiple-scales method which is one of well-known perturbation methods. The harmonically forced Duffing oscillator, the harmonically forced oscillator with both nonlinear restoring force and nonlinear inertial force, the harmonically forced purely nonlinear oscillator and harmonically forced two-degree-of-freedom system with cubic nonlinearity are analyzed in various cases to show the advantages of the proposed method. The ratio of nonlinear stiffness coefficient to linear stiffness coefficient is chosen to be larger than one to highlight the validity of the propose method when dealing with strongly nonlinear oscillators. The validity of the proposed procedure is examined by comparing the frequency–response curves obtained by the proposed method, conventional multiple-scales method and numerical continuation method. Moreover, the errors corresponding to the results obtained by multiple-scales method are compared with those obtained by the proposed method to examine the performance of the proposed method. The results show that the proposed method can give much improved solutions in comparison with those obtained by multiple-scales method.

KeywordMultiple-scales Method Nonlinear Oscillator Optimum Solution Parameter Splitting Strong Nonlinearity
Subject Area力学 ; 工程与技术科学基础学科
DOI10.1007/s11071-019-04887-w
URLView the original
Indexed BySCIE
Language英語English
WOS SubjectMathematics, Applied ; Mechanics
WOS IDWOS:000465507300007
Scopus ID2-s2.0-85064276472
Fulltext Access
Citation statistics
Document TypeJournal article
CollectionDEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING
AffiliationDepartment of Civil and Environmental Engineering,University of Macau,Taipa,China
First Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Du,Hai En,Er,Guo Kang,Iu,Vai Pan. Parameter-splitting perturbation method for the improved solutions to strongly nonlinear systems[J]. Nonlinear Dynamics, 2019, 96, 1847-1863.
APA Du,Hai En., Er,Guo Kang., & Iu,Vai Pan (2019). Parameter-splitting perturbation method for the improved solutions to strongly nonlinear systems. Nonlinear Dynamics, 96, 1847-1863.
MLA Du,Hai En,et al."Parameter-splitting perturbation method for the improved solutions to strongly nonlinear systems".Nonlinear Dynamics 96(2019):1847-1863.
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