Previous research shows that the rotation of non-spherical particles under compression might lead to the effect of apparent negative stiffness. The effect of a rotating non-spherical particle is modeled and it is shown that under displacement-controlled loading its dynamics is equivalent to the dynamics of inverted pendulum. Analytically and experimentally, the eigenfrequency and the stability of the inverted pendulum under changing mass is investigated. It is demonstrated that the increase of total mass leads to the decrease of eigenfrequency of the system beyond that of an ordinary pendulum. Furthermore, there exists a value of the mass when the eigen frequency becomes zero. At this point the system loses its stability. This corresponds to the results obtained for a pair of coupled linear oscillators with one negative stiffness spring. Thus the concept of negative stiffness allows formulation of a simple and accurate model of inverted pendulum and rotating non-spherical particles. It is shown that a set of randomly sized rotating non-spherical particles create fluctuations in the friction force, which can form a mechanism of experimentally observed friction force fluctuations.

We investigate the influence of oscillating normal force on the frictional sliding. Frictional sliding in the case of a simple mass-spring model of Burridge and Knopoff type demonstrates stick-slip even when the friction coefficient is constant. Oscillations of the normal force in this case do not produce noticeable changes in the stick-slip sliding mode. A completely different picture is observed when the oscillations of normal force are applied to the system, which is in the state of steady sliding. In this case the normal oscillations turn the steady sliding into stick slip. A special case is observed when the normal force oscillates with the eigen frequency of the stick-slip motion. Then, no matter how small the amplitude of oscillations is the system reaches the same final stick-slip regime. The time required to reach this limiting regime is inversely proportional to the amplitude of oscillations of the normal force.

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Abstract. Stick-slip sliding is observed at various scales in fault sliding and the accompanied seismic events. It is conventionally assumed that the mechanism of stick-slip over geo-materials lies in the rate dependence of friction. However, the movement resembling the stick-slip could be associated with elastic oscillations of the rock around the fault, which occurs irrespective of the rate properties of the friction. In order to investigate this mechanism, two simple models are considered in this paper: a mass-spring model of selfmaintaining oscillations and a one-dimensional (1-D) model of wave propagation through an infinite elastic rod. The rod slides with friction over a stiff base. The sliding is resisted by elastic shear springs. The results show that the frictional sliding in the mass-spring model generates oscillations that resemble the stick-slip motion. Furthermore, it was observed that the stick-slip-like motion occurs even when the frictional coefficient is constant. The 1-D wave propagation model predicts that despite the presence of shear springs the frictional sliding waves move with the P wave velocity, denoting the wave as intersonic. It was also observed that the amplitude of sliding is decreased with time. This effect might provide an explanation to the observed intersonic rupture propagation over faults.

Abstract. Stick-slip sliding is observed at various scales in fault sliding and the accompanied seismic events. It is conventionally assumed that the mechanism of stick-slip over geomaterials lies in the rate dependence of friction. However, the movement resembling the stick-slip could be associated with elastic oscillations of the rock around the fault, which occurs regardless of rate properties of the friction. In order to investigate this mechanism, two simple models were considered: a mass-spring model of Burridge and Knopoff type (BK model) and a one-dimensional (1D) model an infinite elastic rod driven by elastic shear spring. The results show that frictional sliding in the case of BK model demonstrates stick-slip-like motion even when the friction coefficient is constant. The 1D rod model predicts that any initial disturbance moves with a p-wave velocity, that is supersonically with the amplitude of disturbances decreasing with time. This effect might provide an explanation to the observed supersonic rupture propagation over faults.