Large-Amplitude Elastic Free-Surface Waves: Geometric Nonlinearity and Peakons
| Autor: | Lawrence K. Forbes, S. J. Walters, Anya M. Reading |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Physics
Surface (mathematics) Disturbance (geology) Plane (geometry) Mechanical Engineering FOS: Physical sciences 02 engineering and technology Mechanics Condensed Matter - Soft Condensed Matter 01 natural sciences Peakon 010305 fluids & plasmas Geophysics (physics.geo-ph) Physics - Geophysics Nonlinear system 020303 mechanical engineering & transports Brittleness Amplitude 0203 mechanical engineering Mechanics of Materials Free surface 0103 physical sciences Soft Condensed Matter (cond-mat.soft) General Materials Science |
| Popis: | An instantaneous sub-surface disturbance in a two-dimensional elastic half-space is considered. The disturbance propagates through the elastic material until it reaches the free surface, after which it propagates out along the surface. In conventional theory, the free-surface conditions on the unknown surface are projected onto the flat plane $y = 0$, so that a linear model may be used. Here, however, we present a formulation that takes explicit account of the fact that the location of the free surface is unknown {\it a priori}, and we show how to solve this more difficult problem numerically. This reveals that, while conventional linearized theory gives an accurate account of the decaying waves that travel outwards along the surface, it can under-estimate the strength of the elastic rebound above the location of the disturbance. In some circumstances, the non-linear solution fails in finite time, due to the formation of a ``peakon'' at the free surface. We suggest that brittle failure of the elastic material might in practice be initiated at those times and locations. 26 pages, 7 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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