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

Journal article (2022)

Authors

A.K. Abramian Russian Academy of Sciences (IPME RAS)
S. A. Vakulenko Russian Academy of Sciences (IPME RAS)
W.T. van Horssen Mathematical Physics - EEMCS
Research Group
Mathematical Physics (EEMCS) (TU Delft)
Copyright: © 2022 Andrei K. Abramian, Sergei A. Vakulenko, W.T. van Horssen
DOI: https://doi.org/10.1007/s11071-022-08142-7
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Published Date

2022

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Mathematical Physics

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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