Evaluation of the Autoparametric Pendulum Vibration Absorber for a Duffing System
In this work we study the frequency and dynamic response of a damped Duffing system attached to a parametrically excited pendulum vibration absorber. The multiple scales method is applied to get the autoparametric resonance conditions and the results are compared with a similar application of a pend...
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| Format: | Article |
| Language: | English |
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Wiley
2008-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.1155/2008/827129 |
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| _version_ | 1832562461315694592 |
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| author | Benjamın Vazquez-Gonzalez Gerardo Silva-Navarro |
| author_facet | Benjamın Vazquez-Gonzalez Gerardo Silva-Navarro |
| author_sort | Benjamın Vazquez-Gonzalez |
| collection | DOAJ |
| description | In this work we study the frequency and dynamic response of a damped Duffing system attached to a parametrically excited pendulum vibration absorber. The multiple scales method is applied to get the autoparametric resonance conditions and the results are compared with a similar application of a pendulum absorber for a linear primary system. The approximate frequency analysis reveals that the nonlinear dynamics of the externally excited system are suppressed by the pendulum absorber and, under this condition, the primary Duffing system yields a time response almost equivalent to that obtained for a linear primary system, although the absorber frequency response is drastically modified and affected by the cubic stiffness, thus modifying the jumps defined by the fixed points. In the absorber frequency response can be appreciated a good absorption capability for certain ranges of nonlinear stiffness and the internal coupling is maintained by the existing damping between the pendulum and the primary system. Moreover, the stability of the coupled system is also affected by some extra fixed points introduced by the cubic stiffness, which is illustrated with several amplitude-force responses. Some numerical simulations of the approximate frequency responses and dynamic behavior are performed to show the steady-state and transient responses. |
| format | Article |
| id | doaj-art-3b7127985e534813872b36e6ccde88e5 |
| institution | Kabale University |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-3b7127985e534813872b36e6ccde88e52025-02-03T01:22:30ZengWileyShock and Vibration1070-96221875-92032008-01-01153-435536810.1155/2008/827129Evaluation of the Autoparametric Pendulum Vibration Absorber for a Duffing SystemBenjamın Vazquez-Gonzalez0Gerardo Silva-Navarro1Universidad Autonoma Metropolitana, Plantel Azcapotzalco, Departamento de Energia, Av. San Pablo No. 180, Col. Reynosa Tamaulipas, C.P. 02200 Mexico, D.F., MexicoCentro de Investigacion y de Estudios Avanzados del I. P. N., Departamento de Ingenieria Electrica, Seccion de Mecatronica, A.P. 14-740, C.P. 07360 Mexico, D.F., MexicoIn this work we study the frequency and dynamic response of a damped Duffing system attached to a parametrically excited pendulum vibration absorber. The multiple scales method is applied to get the autoparametric resonance conditions and the results are compared with a similar application of a pendulum absorber for a linear primary system. The approximate frequency analysis reveals that the nonlinear dynamics of the externally excited system are suppressed by the pendulum absorber and, under this condition, the primary Duffing system yields a time response almost equivalent to that obtained for a linear primary system, although the absorber frequency response is drastically modified and affected by the cubic stiffness, thus modifying the jumps defined by the fixed points. In the absorber frequency response can be appreciated a good absorption capability for certain ranges of nonlinear stiffness and the internal coupling is maintained by the existing damping between the pendulum and the primary system. Moreover, the stability of the coupled system is also affected by some extra fixed points introduced by the cubic stiffness, which is illustrated with several amplitude-force responses. Some numerical simulations of the approximate frequency responses and dynamic behavior are performed to show the steady-state and transient responses.http://dx.doi.org/10.1155/2008/827129 |
| spellingShingle | Benjamın Vazquez-Gonzalez Gerardo Silva-Navarro Evaluation of the Autoparametric Pendulum Vibration Absorber for a Duffing System Shock and Vibration |
| title | Evaluation of the Autoparametric Pendulum Vibration Absorber for a Duffing System |
| title_full | Evaluation of the Autoparametric Pendulum Vibration Absorber for a Duffing System |
| title_fullStr | Evaluation of the Autoparametric Pendulum Vibration Absorber for a Duffing System |
| title_full_unstemmed | Evaluation of the Autoparametric Pendulum Vibration Absorber for a Duffing System |
| title_short | Evaluation of the Autoparametric Pendulum Vibration Absorber for a Duffing System |
| title_sort | evaluation of the autoparametric pendulum vibration absorber for a duffing system |
| url | http://dx.doi.org/10.1155/2008/827129 |
| work_keys_str_mv | AT benjamınvazquezgonzalez evaluationoftheautoparametricpendulumvibrationabsorberforaduffingsystem AT gerardosilvanavarro evaluationoftheautoparametricpendulumvibrationabsorberforaduffingsystem |