Residential College | true |
Status | 已發表Published |
Parameter-splitting perturbation method for the improved solutions to strongly nonlinear systems | |
Du,Hai En; Er,Guo Kang; Iu,Vai Pan | |
2019 | |
Source Publication | Nonlinear Dynamics |
ISSN | 1573-269X |
Volume | 96Pages: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. |
Keyword | Multiple-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 |
DOI | 10.1007/s11071-019-04887-w |
URL | View the original |
Indexed By | SCIE |
Language | 英語English |
WOS Subject | Mathematics, Applied ; Mechanics |
WOS ID | WOS:000465507300007 |
Scopus ID | 2-s2.0-85064276472 |
Fulltext Access | |
Citation statistics | |
Document Type | Journal article |
Collection | DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING |
Affiliation | Department of Civil and Environmental Engineering,University of Macau,Taipa,China |
First Author Affilication | University 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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