Oscillations of a string on an elastic foundation with space and time-varying rigidity

A. K. Abramian*, W. T. van Horssen, SA Vakulenko

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

3 Citations (Scopus)
49 Downloads (Pure)


The dynamics of a string on an elastic foundation with time- and coordinate-dependent coefficients have been studied. Asymptotic solutions have been constructed for the following cases: for an arbitrary value of the elastic foundation coefficient at small and large time values, and for small and large coefficients of the elastic foundation at arbitrary times. Also a special case originated from an ageing process has been studied. The ageing process is described by an expression approximating some well-known experimental data. The existence of localized modes along the x coordinate is shown. The existence of these localized modes can lead to a spatial resonance phenomenon under certain conditions. For the case of an arbitrary elastic foundation coefficient value at small and at large times, the spatial resonance phenomenon is observed at small, special frequencies. This effect depends also on a special phase and mode number. For large mode numbers, this special resonance seems to be not possible.

Original languageEnglish
Pages (from-to)567-580
Number of pages14
JournalNonlinear Dynamics: an international journal of nonlinear dynamics and chaos in engineering systems
Issue number1
Publication statusPublished - 2017


  • Ageing
  • Elastic foundation
  • Localized modes
  • Slender structure
  • Thin film
  • Time-varying rigidity


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