Linear stability analysis of the condition for vibration during frictional slip

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