On the Motion of Harmonically Excited Spring Pendulum in Elliptic Path Near Resonances
The response of a nonlinear multidegrees of freedom (M-DOF) for a nature dynamical system represented by a spring pendulum which moves in an elliptic path is investigated. Lagrange’s equations are used in order to derive the governing equations of motion. One of the important perturbation techniques...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2016-01-01
|
| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2016/8734360 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832561306862878720 |
|---|---|
| author | T. S. Amer M. A. Bek I. S. Hamada |
| author_facet | T. S. Amer M. A. Bek I. S. Hamada |
| author_sort | T. S. Amer |
| collection | DOAJ |
| description | The response of a nonlinear multidegrees of freedom (M-DOF) for a nature dynamical system represented by a spring pendulum which moves in an elliptic path is investigated. Lagrange’s equations are used in order to derive the governing equations of motion. One of the important perturbation techniques MS (multiple scales) is utilized to achieve the approximate analytical solutions of these equations and to identify the resonances of the system. Besides, the amplitude and the phase variables are renowned to study the steady-state solutions and to recognize their stability conditions. The time history for the attained solutions and the projections of the phase plane are presented to interpret the behavior of the dynamical system. The mentioned model is considered one of the important scientific applications like in instrumentation, addressing the oscillations occurring in sawing buildings and the most of various applications of pendulum dampers. |
| format | Article |
| id | doaj-art-a2e84d0f42614b9596e8c5b51d99d6be |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-a2e84d0f42614b9596e8c5b51d99d6be2025-02-03T01:25:23ZengWileyAdvances in Mathematical Physics1687-91201687-91392016-01-01201610.1155/2016/87343608734360On the Motion of Harmonically Excited Spring Pendulum in Elliptic Path Near ResonancesT. S. Amer0M. A. Bek1I. S. Hamada2Department of Mathematics, Faculty of Science, Tanta University, Tanta 31527, EgyptDepartment of Physics and Engineering Mathematics, Faculty of Engineering, Tanta University, Tanta 31734, EgyptDepartment of Mathematics, Faculty of Science, Tanta University, Tanta 31527, EgyptThe response of a nonlinear multidegrees of freedom (M-DOF) for a nature dynamical system represented by a spring pendulum which moves in an elliptic path is investigated. Lagrange’s equations are used in order to derive the governing equations of motion. One of the important perturbation techniques MS (multiple scales) is utilized to achieve the approximate analytical solutions of these equations and to identify the resonances of the system. Besides, the amplitude and the phase variables are renowned to study the steady-state solutions and to recognize their stability conditions. The time history for the attained solutions and the projections of the phase plane are presented to interpret the behavior of the dynamical system. The mentioned model is considered one of the important scientific applications like in instrumentation, addressing the oscillations occurring in sawing buildings and the most of various applications of pendulum dampers.http://dx.doi.org/10.1155/2016/8734360 |
| spellingShingle | T. S. Amer M. A. Bek I. S. Hamada On the Motion of Harmonically Excited Spring Pendulum in Elliptic Path Near Resonances Advances in Mathematical Physics |
| title | On the Motion of Harmonically Excited Spring Pendulum in Elliptic Path Near Resonances |
| title_full | On the Motion of Harmonically Excited Spring Pendulum in Elliptic Path Near Resonances |
| title_fullStr | On the Motion of Harmonically Excited Spring Pendulum in Elliptic Path Near Resonances |
| title_full_unstemmed | On the Motion of Harmonically Excited Spring Pendulum in Elliptic Path Near Resonances |
| title_short | On the Motion of Harmonically Excited Spring Pendulum in Elliptic Path Near Resonances |
| title_sort | on the motion of harmonically excited spring pendulum in elliptic path near resonances |
| url | http://dx.doi.org/10.1155/2016/8734360 |
| work_keys_str_mv | AT tsamer onthemotionofharmonicallyexcitedspringpenduluminellipticpathnearresonances AT mabek onthemotionofharmonicallyexcitedspringpenduluminellipticpathnearresonances AT ishamada onthemotionofharmonicallyexcitedspringpenduluminellipticpathnearresonances |