arXiv subjects
Publications and source records attributed to J. Szkutnik.
Numerical simulations are performed for the stick-slip motion in the Burridge-Knopoff model of one block. Calculated amplitude increases with the driving velocity. We argue that this effect can be a criterion to distinguish between the stick-slip and pure slip oscillations.
A three-blocks Burridge-Knopoff model is investigated. The dimensionless velocity-dependent friction force $F(v)\propto (1+av)^{-1}$ is linearized around $a=0$. In this way, the model is transformed into a six-dimensional mapping $\mathbf{x}(t_{n})\to \mathbf{x}(t_{n+1})$, where $t_n$ are time moments when a block starts to move or stops. Between these moments, the equations of motion are integrable. For $a<0.1$, the motion is quasiperiodic or periodic, depending on the initial conditions. For the periodic solution, we observe a synchronization of the motion of the lateral blocks. For $a>0.1$, the motion becomes chaotic. These results are true for the linearized mapping, linearized numerical and non-linearized numerical solutions.