Lyapunov Equivalent Representation Form of Forced, Damped, Nonlinear, Two Degree-of-Freedom Systems
The aim of this paper focuses on finding equivalent representation forms of forced, damped, two degree-of-freedom, nonlinear systems in the sense of Lyapunov by using a nonlinear transformation approach that provides decoupled, forced, damped, nonlinear equations of the Duffing type, under the assum...
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| Format: | Article |
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MDPI AG
2018-04-01
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| Series: | Applied Sciences |
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| Online Access: | http://www.mdpi.com/2076-3417/8/4/649 |
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| author | Alex Elías-Zúñiga Luis M. Palacios-Pineda Daniel Olvera-Trejo Oscar Martínez-Romero |
| author_facet | Alex Elías-Zúñiga Luis M. Palacios-Pineda Daniel Olvera-Trejo Oscar Martínez-Romero |
| author_sort | Alex Elías-Zúñiga |
| collection | DOAJ |
| description | The aim of this paper focuses on finding equivalent representation forms of forced, damped, two degree-of-freedom, nonlinear systems in the sense of Lyapunov by using a nonlinear transformation approach that provides decoupled, forced, damped, nonlinear equations of the Duffing type, under the assumption that the driving frequency and the external forces are equal in both systems. The values of Lyapunov characteristic exponents (LCEs), Lyapunov largest exponents (LLE), and time-amplitude and frequency-amplitude curves computed from numerical integration solutions, indicate that the decoupled Duffing-type equations are equivalent, in the sense of Lyapunov, to the original dynamic system, since both set of motion equations tend to have the same qualitative and quantitative behaviors. |
| first_indexed | 2024-04-14T02:49:01Z |
| format | Article |
| id | doaj.art-5b21205ec34d413f937141bea437cf80 |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-04-14T02:49:01Z |
| publishDate | 2018-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj.art-5b21205ec34d413f937141bea437cf802022-12-22T02:16:24ZengMDPI AGApplied Sciences2076-34172018-04-018464910.3390/app8040649app8040649Lyapunov Equivalent Representation Form of Forced, Damped, Nonlinear, Two Degree-of-Freedom SystemsAlex Elías-Zúñiga0Luis M. Palacios-Pineda1Daniel Olvera-Trejo2Oscar Martínez-Romero3Escuela de Ingeniería y Ciencias, Tecnologico de Monterrey, Ave. Eugenio Garza Sada 2501, Monterrey, N.L., C.P. 64849, MexicoDivisión de Estudios de Posgrado e Investigación, Tecnológico Nacional de México/Instituto Tecnológico de Pachuca, Carr. México-Pachuca Km 87.5, Pachuca, Hidalgo, C.P. 42080, MexicoEscuela de Ingeniería y Ciencias, Tecnologico de Monterrey, Ave. Eugenio Garza Sada 2501, Monterrey, N.L., C.P. 64849, MexicoEscuela de Ingeniería y Ciencias, Tecnologico de Monterrey, Ave. Eugenio Garza Sada 2501, Monterrey, N.L., C.P. 64849, MexicoThe aim of this paper focuses on finding equivalent representation forms of forced, damped, two degree-of-freedom, nonlinear systems in the sense of Lyapunov by using a nonlinear transformation approach that provides decoupled, forced, damped, nonlinear equations of the Duffing type, under the assumption that the driving frequency and the external forces are equal in both systems. The values of Lyapunov characteristic exponents (LCEs), Lyapunov largest exponents (LLE), and time-amplitude and frequency-amplitude curves computed from numerical integration solutions, indicate that the decoupled Duffing-type equations are equivalent, in the sense of Lyapunov, to the original dynamic system, since both set of motion equations tend to have the same qualitative and quantitative behaviors.http://www.mdpi.com/2076-3417/8/4/649Lyapunov characteristic exponentsDuffing’s equationfrequency amplitude response curvesinternal resonances |
| spellingShingle | Alex Elías-Zúñiga Luis M. Palacios-Pineda Daniel Olvera-Trejo Oscar Martínez-Romero Lyapunov Equivalent Representation Form of Forced, Damped, Nonlinear, Two Degree-of-Freedom Systems Applied Sciences Lyapunov characteristic exponents Duffing’s equation frequency amplitude response curves internal resonances |
| title | Lyapunov Equivalent Representation Form of Forced, Damped, Nonlinear, Two Degree-of-Freedom Systems |
| title_full | Lyapunov Equivalent Representation Form of Forced, Damped, Nonlinear, Two Degree-of-Freedom Systems |
| title_fullStr | Lyapunov Equivalent Representation Form of Forced, Damped, Nonlinear, Two Degree-of-Freedom Systems |
| title_full_unstemmed | Lyapunov Equivalent Representation Form of Forced, Damped, Nonlinear, Two Degree-of-Freedom Systems |
| title_short | Lyapunov Equivalent Representation Form of Forced, Damped, Nonlinear, Two Degree-of-Freedom Systems |
| title_sort | lyapunov equivalent representation form of forced damped nonlinear two degree of freedom systems |
| topic | Lyapunov characteristic exponents Duffing’s equation frequency amplitude response curves internal resonances |
| url | http://www.mdpi.com/2076-3417/8/4/649 |
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