Dynamic Instability of Two Elastic Half-Spaces Sliding With a Rate-and-State Friction Constitutive Law

2016 ◽  
Vol 83 (12) ◽  
Author(s):  
Jérôme Colin
Keyword(s):  
Dynamic Instability ◽  
Constitutive Law ◽  
Steady State Regime ◽  
Stick Slip ◽  
Slip Regime ◽  
Rate And State Friction ◽  
Modulus Difference ◽  
State Regime ◽  
Loss Of Contact ◽  
Elastic Coefficients

The destabilization of the steady-state regime of two semi-infinite half-spaces of different elastic coefficients sliding upon each other has been theoretically investigated when a rate-and-state friction constitutive law controls the sliding. In the framework of linear and isotropic elastodynamics, the effect of the frictional constitutive law has been investigated onto the development of self-excited oscillations as well as the influence of the shear modulus difference between the two materials. The possibility of existence of a stick–slip regime and the conditions for the loss-of-contact are finally discussed.

scholarly journals Triggering avalanches by transverse perturbations in a rotating drum

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Vicente Salinas ◽  
Cristóbal Quiñinao ◽  
Sebastián González ◽  
Gustavo Castillo
Keyword(s):  
Hopf Bifurcation ◽  
Theoretical Model ◽  
Order Parameter ◽  
Small Scale ◽  
Rotating Drum ◽  
Governing Parameter ◽  
Stick Slip ◽  
Slip Regime ◽  
Axis Of Rotation

AbstractWe study the role of small-scale perturbations in the onset of avalanches in a rotating drum in the stick-slip regime. By vibrating the system along the axis of rotation with an amplitude orders of magnitude smaller than the particles’ diameter, we found that the order parameter that properly describes the system is the kinetic energy. We also show that, for high enough frequencies, the onset of the avalanche is determined by the amplitude of the oscillation, contrary to previous studies that showed that either acceleration or velocity was the governing parameter. Finally, we present a theoretical model that explains the transition between the continuous and discrete avalanche regimes as a supercritical Hopf bifurcation.

GRANULAR FAILURE: THE ORIGIN OF EARTHQUAKES?

2009 ◽  
Vol 23 (28n29) ◽  
pp. 5374-5382 ◽  
Author(s):  
MASSIMO PICA CIAMARRA ◽  
LUCILLA DE ARCANGELIS ◽  
EUGENIO LIPPIELLO ◽  
CATALDO GODANO
Keyword(s):  
Confining Pressure ◽  
Stick Slip ◽  
Slip Regime ◽  
Constant Rate ◽  
Large Fluctuations ◽  
System Flow ◽  
System Phase Diagram ◽  
Dynamics Simulations ◽  
Stick Slip Motion ◽  
System Phase

Via Molecular Dynamics simulations, we investigate the stick-slip motion in a model of fault, where two surfaces subject to a constant confining pressure P, and enclosing granular particles, are subject a shear stress σ. When the system sticks, the stress increases with a constant rate [Formula: see text], while the stress decreases when the system flow. We dermine the system 'phase diagram' in the pressure P load velocity [Formula: see text] plane, locating the transition form the continuos flow regime to the stick-slip regimes, and show that the transition between these two regimes is characterized by the presence of large fluctuations. In the stick-slip regime, the system reproduces the behaviour of a segment of a fault of fixed lenght.

Experimental Investigation of Power Umbilical Damping

2017 ◽  
Author(s):  
Torfinn Ottesen
Keyword(s):  
Steady State ◽  
Energy Input ◽  
State Energy ◽  
Seawater Temperature ◽  
Structural Damping ◽  
Stick Slip ◽  
Slip Regime ◽  
Free Decay ◽  
Vortex Induced Vibrations ◽  
Slip Transition

Ocean currents may cause vortex induced vibrations (VIV) of deep-water umbilicals and cables. Since the VIV response may give significant contributions to the total fatigue damage it is important to know the structural damping for relevant curvature levels. A laboratory test has been performed on a 12.5 m long test specimen to determine the damping for a range of curvature levels that are in the vicinity of the stick-slip transition region. The energy input to maintain steady state oscillations with curvature amplitudes in the range 0.0002–0.001 m−1 was measured. The steady state energy input is consistent with damping ratios obtained using the free decay method. The structural damping depends on construction temperature and curvature and is less for typically low seawater temperature and low curvatures. The transition between the stick- and the slip regime is seen for typical seawater temperature.

Dissipative and Generative Fractional Electric Elements in Modeling RC and RL Circuits

2021 ◽  
Author(s):  
Kristian Haška ◽  
Stevan Cvetićanin ◽  
Dušan Zorica
Keyword(s):  
Asymptotic Behavior ◽  
Steady State ◽  
Constitutive Equation ◽  
Magnetic Flux ◽  
Electromotive Force ◽  
Constitutive Models ◽  
Steady State Regime ◽  
Power Type ◽  
State Regime ◽  
Transient And Steady State

Abstract Generalized capacitor (inductor) is constitutively modeled by expressing charge (magnetic flux) in terms of voltage (current) memory as a sum of instantaneous and power type hereditary contributions and it is proved to be a dissipative electric element by thermodynamic analysis. On the contrary, generalized capacitor (inductor) as a generative electric element is modeled using the same form of the constitutive equation, but by expressing voltage (current) in terms of charge (magnetic flux) memory. These constitutive models are used in transient and steady state regime analysis of the series RC and RL circuits subject to electromotive force, as well as in the study of circuits' frequency characteristics including asymptotic behavior.

scholarly journals On the mathematical model of combined rarefaction and compression waves in condensed matter

2021 ◽  
Vol 50 ◽  
pp. 104-107
Author(s):  
Alexander Alexandrovitch Samokhin ◽  
Pavel Aleksandrovich Pivovarov
Keyword(s):  
Shock Wave ◽  
Rarefaction Wave ◽  
Condensed Matter ◽  
Steady State Regime ◽  
Compression Waves ◽  
Momentum Fluxes ◽  
State Regime ◽  
The Mathematical Model ◽  
The Waves ◽  
Nonmetal Transition

Two waves model where shock wave is combined with rarefaction wave appearing in laser ablation due to metal-nonmetal transition effect is investigated using conservation laws for mass and momentum fluxes for the steady-state regime of the process. This approach permits to obtain the relation between front velocities of the waves which shows that the rarefaction wave can be rather slow compared with the generated shock wave.

scholarly journals Simulation of a two-dimensional binary gas mixture outflow into vacuum through a thin slit on the basis of direct solution of the Boltzmann kinetic equation

2021 ◽  
Vol 2056 (1) ◽  
pp. 012007
Author(s):  
S S Sitnikov ◽  
F G Tcheremissine ◽  
T A Sazykina
Keyword(s):  
Kinetic Equation ◽  
Boltzmann Kinetic Equation ◽  
Gas Mixture ◽  
Two Dimensional ◽  
Direct Solution ◽  
Steady State Regime ◽  
Collision Integrals ◽  
Flow Formation ◽  
Binary Gas Mixture ◽  
State Regime

Abstract Two-dimensional binary gas mixture outflow from a vessel into vacuum through a thin slit is studied on the basis of direct solution of the Boltzmann kinetic equation. For evaluation of collision integrals in the Boltzmann equation a conservative projection method is used. Numerical simulation of a two-dimensional argon-neon gas mixture outflow from a vessel into vacuum was performed. Graphs of mixture components flow rate dependence on time during the flow formation, as well as fields of molecular density and temperature for steady-state regime, were obtained.

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