Dynamics of a weakly nonlinear string on an elastic foundation with a partly prescribed discrete spectrum

Andrei K. Abramian; Sergei A. Vakulenko; Wim T. van Horssen

doi:10.1007/s11071-022-08142-7

Dynamics of a weakly nonlinear string on an elastic foundation with a partly prescribed discrete spectrum

Andrei K. Abramian^*, Sergei A. Vakulenko, Wim T. van Horssen

^*Corresponding author for this work

Mathematical Physics

Research output: Contribution to journal › Article › Scientific › peer-review

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Abstract

In this paper the dynamics of a weakly nonlinear elastic string on a Winkler elastic foundation is studied. The foundation may be spatially heterogeneous. At one end of the string a mass-spring system is attached, and the other end of the string is fixed. The string is assumed to be long, and the lower part of the spectrum of the string is prescribed. It is shown that localized modes exist and that the dynamics of the string for large times is determined by these localized modes. The frequencies of these localized modes can be controlled by special choices for the spatial heterogeneities in the elastic foundation. Analytical and numerical results are presented to illustrate the findings.

Original language	English
Pages (from-to)	5221-5235
Number of pages	15
Journal	Nonlinear Dynamics
Volume	111
Issue number	6
DOIs	https://doi.org/10.1007/s11071-022-08142-7
Publication status	Published - 2022

Bibliographical note

Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Keywords

Inhomogeneous Winkler foundation
Nonlinear string
Prescribed spectrum

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10.1007/s11071-022-08142-7

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Cite this

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title = "Dynamics of a weakly nonlinear string on an elastic foundation with a partly prescribed discrete spectrum",

abstract = "In this paper the dynamics of a weakly nonlinear elastic string on a Winkler elastic foundation is studied. The foundation may be spatially heterogeneous. At one end of the string a mass-spring system is attached, and the other end of the string is fixed. The string is assumed to be long, and the lower part of the spectrum of the string is prescribed. It is shown that localized modes exist and that the dynamics of the string for large times is determined by these localized modes. The frequencies of these localized modes can be controlled by special choices for the spatial heterogeneities in the elastic foundation. Analytical and numerical results are presented to illustrate the findings.",

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note = "Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.",

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doi = "10.1007/s11071-022-08142-7",

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AU - Vakulenko, Sergei A.

AU - van Horssen, Wim T.

N1 - Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

PY - 2022

Y1 - 2022

N2 - In this paper the dynamics of a weakly nonlinear elastic string on a Winkler elastic foundation is studied. The foundation may be spatially heterogeneous. At one end of the string a mass-spring system is attached, and the other end of the string is fixed. The string is assumed to be long, and the lower part of the spectrum of the string is prescribed. It is shown that localized modes exist and that the dynamics of the string for large times is determined by these localized modes. The frequencies of these localized modes can be controlled by special choices for the spatial heterogeneities in the elastic foundation. Analytical and numerical results are presented to illustrate the findings.

AB - In this paper the dynamics of a weakly nonlinear elastic string on a Winkler elastic foundation is studied. The foundation may be spatially heterogeneous. At one end of the string a mass-spring system is attached, and the other end of the string is fixed. The string is assumed to be long, and the lower part of the spectrum of the string is prescribed. It is shown that localized modes exist and that the dynamics of the string for large times is determined by these localized modes. The frequencies of these localized modes can be controlled by special choices for the spatial heterogeneities in the elastic foundation. Analytical and numerical results are presented to illustrate the findings.

KW - Inhomogeneous Winkler foundation

KW - Nonlinear string

KW - Prescribed spectrum

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DO - 10.1007/s11071-022-08142-7

M3 - Article

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SN - 0924-090X

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EP - 5235

JO - Nonlinear Dynamics

JF - Nonlinear Dynamics

IS - 6

ER -

Dynamics of a weakly nonlinear string on an elastic foundation with a partly prescribed discrete spectrum

Abstract

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Keywords

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