Stick slip dynamics model

F. Heslot, T. Baumberger, B. Caroli, and C Caroli, Creep, Stick-slip and Dry Friction Dynamics Experiments and a Heuristic Model, Phys. Rev., E49, 4973 (1994). 

We discuss the various dynamical models of earthquake-like failures in Chapter 4. Specifically, the properties of the Burridge-Knopoff stick-slip model (Burridge and Knopoff 1967) and of the self-organised criticality models, the Guttenberg-Richter type power laws, for the frequency distribution of earthquakes in these models are discussed here. 

Dynamics, Fig. 12 Mechanical model for the stick-slip phenomenon... 

Yet another theory has emerged recently from the field of nanotribology. Surface force apparatus studies, combined with molecular dynamics simulations, of simplified model systems, such as molecularly flat mica separated by a few molecules thick lubricant layers, have identified a solid-melt transition as the cause for stick-slip motion to occur for such confined liquids (18, 106, 111-113, 144-149). A similarly confined liquid can be found in macroscopic friction systems in the boundary lubrication regime wherein thin lubricant layers are trapped between surface asperities in very close proximity. 

The inclusion of the all-purpose rigid-body dynamic model in the design and control improves the mechanical system behaviour and performance fidelity. However, friction imposes additional nonlinearity in the dynamic equations of connected moving bodies. The discontinuous nature of all kinds of friction causes vibrations and stick-slip effects which limit the accuracy of end-effector position or path. 

Bray Travasarou used a nonlinear fully coupled stick-shp shding block model, essentially the Newmark idealization with a deformable slope mass, to capture the dynamic performance of an earth dam, natural slope, or earth fill during earthquake loading. The nonlinear coupled stick-slip deformable shding model is characterized by i) its... 

Recent experiments [1005] with high time resolution have revealed fine structures of the jump dynamics, which cannot be explained by a simple Prandd-Tomlinson model. This has led to the postulation of a new model that assumes an ultrasmall effective mass for the tip apex, which therefore exhibits a much faster kinetics than assumed in previous models [1006,1007]. This led to thermal delocalization of the tip that probes the surface potential at a much faster rate than the observed stick-slip motion of the cantilever. 

Ions in Clays, Fig. 2 Electro-osmotic flow profile between two Na-montmorillonite surfaces separated by a 4.5-mn pore containing water. Reference molecular dynamics (MD) simulations allow to test the validity of continuous models based on the Navier-Stokes (NS) and Poisson-Boltzmann (PB) equations. Such equations must be solved for given boundary conditions (stick or slip) at the solid/liquid interface... 

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