Duffing-type oscillator under harmonic excitation with a variable value of excitation amplitude and time-dependent external disturbances

Abstract For more complex nonlinear systems, where the amplitude of excitation can vary in time or where time-dependent external disturbances appear, an analysis based on the frequency response curve may be insufficient. In this paper, a new tool to analyze nonlinear dynamical systems is proposed as...

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Autor principal:	Wojciech Wawrzynski
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/05ddeede28d940879594fd06c27e1e61
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spelling	oai:doaj.org-article:05ddeede28d940879594fd06c27e1e612021-12-02T14:06:19ZDuffing-type oscillator under harmonic excitation with a variable value of excitation amplitude and time-dependent external disturbances10.1038/s41598-021-82652-z2045-2322https://doaj.org/article/05ddeede28d940879594fd06c27e1e612021-02-01T00:00:00Zhttps://doi.org/10.1038/s41598-021-82652-zhttps://doaj.org/toc/2045-2322Abstract For more complex nonlinear systems, where the amplitude of excitation can vary in time or where time-dependent external disturbances appear, an analysis based on the frequency response curve may be insufficient. In this paper, a new tool to analyze nonlinear dynamical systems is proposed as an extension to the frequency response curve. A new tool can be defined as the chart of bistability areas and area of unstable solutions of the analyzed system. In the paper, this tool is discussed on the basis of the classic Duffing equation. The numerical approach was used, and two systems were tested. Both systems are softening, but the values of the coefficient of nonlinearity are significantly different. Relationships between both considered systems are presented, and problems of the nonlinearity coefficient and damping influence are discussed.Wojciech WawrzynskiNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-15 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Wojciech Wawrzynski Duffing-type oscillator under harmonic excitation with a variable value of excitation amplitude and time-dependent external disturbances
description	Abstract For more complex nonlinear systems, where the amplitude of excitation can vary in time or where time-dependent external disturbances appear, an analysis based on the frequency response curve may be insufficient. In this paper, a new tool to analyze nonlinear dynamical systems is proposed as an extension to the frequency response curve. A new tool can be defined as the chart of bistability areas and area of unstable solutions of the analyzed system. In the paper, this tool is discussed on the basis of the classic Duffing equation. The numerical approach was used, and two systems were tested. Both systems are softening, but the values of the coefficient of nonlinearity are significantly different. Relationships between both considered systems are presented, and problems of the nonlinearity coefficient and damping influence are discussed.
format	article
author	Wojciech Wawrzynski
author_facet	Wojciech Wawrzynski
author_sort	Wojciech Wawrzynski
title	Duffing-type oscillator under harmonic excitation with a variable value of excitation amplitude and time-dependent external disturbances
title_short	Duffing-type oscillator under harmonic excitation with a variable value of excitation amplitude and time-dependent external disturbances
title_full	Duffing-type oscillator under harmonic excitation with a variable value of excitation amplitude and time-dependent external disturbances
title_fullStr	Duffing-type oscillator under harmonic excitation with a variable value of excitation amplitude and time-dependent external disturbances
title_full_unstemmed	Duffing-type oscillator under harmonic excitation with a variable value of excitation amplitude and time-dependent external disturbances
title_sort	duffing-type oscillator under harmonic excitation with a variable value of excitation amplitude and time-dependent external disturbances
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/05ddeede28d940879594fd06c27e1e61
work_keys_str_mv	AT wojciechwawrzynski duffingtypeoscillatorunderharmonicexcitationwithavariablevalueofexcitationamplitudeandtimedependentexternaldisturbances
_version_	1718392002861596672

Duffing-type oscillator under harmonic excitation with a variable value of excitation amplitude and time-dependent external disturbances

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