The dynamical analysis for the motion of a harmonically two degrees of freedom damped spring pendulum in an elliptic trajectory

This article investigates the motion of two degrees of freedom non-linear dynamical system represented by a spring pendulum in which its suspension point moves in an elliptic trajectory. Lagrange's equations are utilized to derive the governing equations of motion in light of the generalized co...

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Autores principales:	T.S. Amer, M.A. Bek, S.S. Hassan
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2022
Materias:	Non-linear vibrations Perturbation methods Fixed points Stability Engineering (General). Civil engineering (General) TA1-2040
Acceso en línea:	https://doaj.org/article/8718d939eee64fb7a3164dd5f6293f59
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spelling	oai:doaj.org-article:8718d939eee64fb7a3164dd5f6293f592021-11-20T04:56:12ZThe dynamical analysis for the motion of a harmonically two degrees of freedom damped spring pendulum in an elliptic trajectory1110-016810.1016/j.aej.2021.06.063https://doaj.org/article/8718d939eee64fb7a3164dd5f6293f592022-02-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S1110016821004245https://doaj.org/toc/1110-0168This article investigates the motion of two degrees of freedom non-linear dynamical system represented by a spring pendulum in which its suspension point moves in an elliptic trajectory. Lagrange's equations are utilized to derive the governing equations of motion in light of the generalized coordinates of this system. The asymptotic solutions for the governing equations of motion up to the third approximation are obtained using the multiple scales technique. The different resonance cases are classified according to the modulation equations. The steady-state solutions are verified in the presence of the solvability conditions. The time histories of the considered motion, the resonance curves, and steady-state solutions are presented graphically. In addition to the simulations of the non-linear equations of the system's evolution, the stability criteria are carried out. The stability and instability regions are investigated, in which it is found the behaviour of the system is stable for a large number of the system’s parameters. In various engineering applications, a better understanding of the vibrational motion near resonance is critical, in which it can be avoided continued exposure to events that can cause severe damage.T.S. AmerM.A. BekS.S. HassanElsevierarticleNon-linear vibrationsPerturbation methodsFixed pointsStabilityEngineering (General). Civil engineering (General)TA1-2040ENAlexandria Engineering Journal, Vol 61, Iss 2, Pp 1715-1733 (2022)
institution	DOAJ
collection	DOAJ
language	EN
topic	Non-linear vibrations Perturbation methods Fixed points Stability Engineering (General). Civil engineering (General) TA1-2040
spellingShingle	Non-linear vibrations Perturbation methods Fixed points Stability Engineering (General). Civil engineering (General) TA1-2040 T.S. Amer M.A. Bek S.S. Hassan The dynamical analysis for the motion of a harmonically two degrees of freedom damped spring pendulum in an elliptic trajectory
description	This article investigates the motion of two degrees of freedom non-linear dynamical system represented by a spring pendulum in which its suspension point moves in an elliptic trajectory. Lagrange's equations are utilized to derive the governing equations of motion in light of the generalized coordinates of this system. The asymptotic solutions for the governing equations of motion up to the third approximation are obtained using the multiple scales technique. The different resonance cases are classified according to the modulation equations. The steady-state solutions are verified in the presence of the solvability conditions. The time histories of the considered motion, the resonance curves, and steady-state solutions are presented graphically. In addition to the simulations of the non-linear equations of the system's evolution, the stability criteria are carried out. The stability and instability regions are investigated, in which it is found the behaviour of the system is stable for a large number of the system’s parameters. In various engineering applications, a better understanding of the vibrational motion near resonance is critical, in which it can be avoided continued exposure to events that can cause severe damage.
format	article
author	T.S. Amer M.A. Bek S.S. Hassan
author_facet	T.S. Amer M.A. Bek S.S. Hassan
author_sort	T.S. Amer
title	The dynamical analysis for the motion of a harmonically two degrees of freedom damped spring pendulum in an elliptic trajectory
title_short	The dynamical analysis for the motion of a harmonically two degrees of freedom damped spring pendulum in an elliptic trajectory
title_full	The dynamical analysis for the motion of a harmonically two degrees of freedom damped spring pendulum in an elliptic trajectory
title_fullStr	The dynamical analysis for the motion of a harmonically two degrees of freedom damped spring pendulum in an elliptic trajectory
title_full_unstemmed	The dynamical analysis for the motion of a harmonically two degrees of freedom damped spring pendulum in an elliptic trajectory
title_sort	dynamical analysis for the motion of a harmonically two degrees of freedom damped spring pendulum in an elliptic trajectory
publisher	Elsevier
publishDate	2022
url	https://doaj.org/article/8718d939eee64fb7a3164dd5f6293f59
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The dynamical analysis for the motion of a harmonically two degrees of freedom damped spring pendulum in an elliptic trajectory

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