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Abstract
Sliding frictional interfaces at a range of length scales are observed to generate travelling waves; these are considered relevant, for example, to both earthquake ground surface movements and the performance of mechanical brakes and dampers. We propose an explanation of the origins of these waves through the study of an idealized mechanical model: a thin elastic plate subject to uniform shear stress held in frictional contact with a rigid flat surface. We construct a nonlinear wave equation for the deformation of the plate, and couple it to a spinodal rate-and-state friction law which leads to a mathematically well-posed problem that is capable of capturing many effects not accessible in a Coulomb friction model. Our model sustains a rich variety of solutions, including periodic stick-slip wave trains, isolated slip and stick pulses, and detachment and attachment fronts. Analytical and numerical bifurcation analysis is used to show how these states are organized in a two-parameter state diagram. We discuss briefly the possible physical interpretation of each of these states, and remark also that our spinodal friction law, though more complicated than other classical rate-and-state laws, is required in order to capture the full richness of wave types.
Original language | English |
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Article number | 0606 |
Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |
Volume | 473 |
Issue number | 2203 |
DOIs | |
Publication status | Published - 1 Jul 2017 |
Research Groups and Themes
- Engineering Mathematics Research Group
Keywords
- Detachment front
- Friction
- Global bifurcation
- Rate-and-state
- Self-healing slip pulse
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Dive into the research topics of 'A phase-plane analysis of localized frictional waves'. Together they form a unique fingerprint.Projects
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Profiles
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Professor Alan R Champneys
- School of Engineering Mathematics and Technology - Professor of Applied Non-linear Mathematics
- Cabot Institute for the Environment
- Systems Centre
Person: Academic , Member