On the Motion of Harmonically Excited Spring Pendulum in Elliptic Path Near Resonances

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...

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Main Authors: T. S. Amer, M. A. Bek, I. S. Hamada
Format: Article
Language:English
Published: Hindawi Limited 2016-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2016/8734360
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spelling doaj-a2e84d0f42614b9596e8c5b51d99d6be2021-07-02T01:02:59ZengHindawi LimitedAdvances 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
collection DOAJ
language English
format Article
sources DOAJ
author T. S. Amer
M. A. Bek
I. S. Hamada
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
author_facet T. S. Amer
M. A. Bek
I. S. Hamada
author_sort T. S. Amer
title 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_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_sort on the motion of harmonically excited spring pendulum in elliptic path near resonances
publisher Hindawi Limited
series Advances in Mathematical Physics
issn 1687-9120
1687-9139
publishDate 2016-01-01
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.
url http://dx.doi.org/10.1155/2016/8734360
work_keys_str_mv AT tsamer onthemotionofharmonicallyexcitedspringpenduluminellipticpathnearresonances
AT mabek onthemotionofharmonicallyexcitedspringpenduluminellipticpathnearresonances
AT ishamada onthemotionofharmonicallyexcitedspringpenduluminellipticpathnearresonances
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