A phase-plane analysis of localized frictional waves

Area of Science:

• Physics
• Mechanical Engineering
• Geophysics

Background:

• Sliding frictional interfaces generate traveling waves across various scales.
• These waves are relevant to phenomena like earthquake ground motion and mechanical brake performance.

Purpose of the Study:

• To propose an explanation for the origin of traveling waves at sliding interfaces.
• To study an idealized mechanical model of a shear-stressed elastic plate in frictional contact.

Main Methods:

• Constructed a nonlinear wave equation for plate deformation.
• Coupled the wave equation to a spinodal rate-and-state friction law.
• Employed analytical and numerical bifurcation analysis to study model solutions.

Main Results:

• The model sustains diverse solutions: periodic stick-slip wave trains, isolated slip/stick pulses, and detachment/attachment fronts.
• A two-parameter state diagram organizes these complex wave states.
• The spinodal friction law is crucial for capturing the full range of wave types.

Conclusions:

• The proposed model provides a framework for understanding traveling waves at frictional interfaces.
• The spinodal friction law offers a more comprehensive description than traditional Coulomb friction models.
• The study highlights the rich dynamics of wave generation in sliding systems.