Linear stability analysis of the condition for vibration during frictional slip

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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.
Original languageEnglish
Article number104993
Pages (from-to)1-10
Number of pages10
JournalJournal of the Mechanics and Physics of Solids
Early online date18 Jun 2022
Publication statusPublished (in print/issue) - 1 Oct 2022

Bibliographical note

Funding Information:
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 .

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© 2022


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