Print Email Facebook Twitter Oscillations of a string on an elastic foundation with space and time-varying rigidity Title Oscillations of a string on an elastic foundation with space and time-varying rigidity Author Abramian, A. (Russian Academy of Sciences) van Horssen, W.T. (TU Delft Mathematical Physics) Vakulenko, SA (ITMO University) Date 2017 Abstract 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. Subject AgeingElastic foundationLocalized modesSlender structureThin filmTime-varying rigidity To reference this document use: http://resolver.tudelft.nl/uuid:eeb1aa9b-39dd-45c8-a7a5-9d64550bc2d4 DOI https://doi.org/10.1007/s11071-016-3261-8 ISSN 0924-090X Source Nonlinear Dynamics: an international journal of nonlinear dynamics and chaos in engineering systems, 88 (1), 567-580 Part of collection Institutional Repository Document type journal article Rights © 2017 A. Abramian, W.T. van Horssen, SA Vakulenko Files PDF 10473664.pdf 728.82 KB Close viewer /islandora/object/uuid:eeb1aa9b-39dd-45c8-a7a5-9d64550bc2d4/datastream/OBJ/view