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Linear stability analysis of the condition for vibration during frictional slip

Im, Kyungjae and Avouac, Jean-Philippe (2022) Linear stability analysis of the condition for vibration during frictional slip. Journal of the Mechanics and Physics of Solids, 167 . Art. No. 104993. ISSN 0022-5096. doi:10.1016/j.jmps.2022.104993.

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Slip along a frictional contact between elastic bodies can be stable or unstable, leading to stick-slip motion. Frictional slip can also be associated with vibrations. The condition for these vibrations and their characteristics remains poorly understood. To address this issue, which is relevant to engineering and earth science, we carry out a linear stability analysis of a spring-and-slider system obeying rate and state friction. We first identify the solution space for the linearized equation and define the conditions for different slip modes from the real and imaginary parts of the solution. We then derive asymptotic equations for all boundaries between overdamped stable sliding, inertial/non-inertial underdamped oscillation, stick-slip, and harmonic vibration. Finally, we verified the conditions with numerical simulations. Our work provides rigorous criteria regarding the conditions for the various frictional slip modes and the emergence of vibrations. It can help design appropriate approaches for suppressing undesired vibrations in mechanical systems and investigate the mechanisms generating vibrations (tremor) associated with fault slip in nature.

Item Type:Article
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URLURL TypeDescription
Im, Kyungjae0000-0003-0057-3119
Avouac, Jean-Philippe0000-0002-3060-8442
Additional Information:© 2022 The Authors. Published by Elsevier Under a Creative Commons license - Attribution 4.0 International (CC BY 4.0). Received 29 March 2022, Revised 8 June 2022, Accepted 17 June 2022, Available online 18 June 2022, Version of Record 1 July 2022. We thank one anonymous reviewer for the insightful comments and suggestions. We also benefitted from discussions with Rob Viesca. This study was supported by the National Science Foundation via the IUCR center Geomechanics and Mitigation of Geohazards (award #1822214) and NSF/EAR award #1821853. Data Availability. No data was used for the research described in the article. CRediT authorship contribution statement. Kyungjae Im: Conceptualization, Methodology, Software, Writing – original draft. Jean-Philippe Avouac: Conceptualization, Validation, Writing – review & editing. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Group:Center for Geomechanics and Mitigation of Geohazards (GMG), Division of Geological and Planetary Sciences, Seismological Laboratory
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Center for Geomechanics and Mitigation of GeohazardsUNSPECIFIED
Record Number:CaltechAUTHORS:20220705-346508000
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Official Citation:Kyungjae Im, Jean-Philippe Avouac, Linear stability analysis of the condition for vibration during frictional slip, Journal of the Mechanics and Physics of Solids, Volume 167, 2022, 104993, ISSN 0022-5096,
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:115324
Deposited By: George Porter
Deposited On:08 Jul 2022 00:16
Last Modified:15 Nov 2022 15:13

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