Nonlinear Dynamic Analysis of Rotor Rub-Impact System

A dynamic model of a double-disk rub-impact rotor-bearing system with rubbing fault is established. The dynamic differential equation of the system is solved by combining the numerical integration method with MATLAB. And the influence of rotor speed, disc eccentricity, and stator stiffness on the response of the rotor-bearing system is analyzed. In the rotor system, the time history diagram, the axis locus diagram, the phase diagram, and the Poincaré section diagram in different rotational speeds are drawn. The characteristics of the periodic motion, quasiperiodic motion, and chaotic motion of the system in a given speed range are described in detail. The ways of the system entering and leaving chaos are revealed. The transformation and evolution process of the periodic motion, quasiperiodic motion, and chaotic motion are also analyzed. It shows that the rotor system enters chaos by the way of the period-doubling bifurcation. With the increase of the eccentricity, the quasi-periodicity evolution is chaotic. The quasiperiodic motion evolves into the periodic three motion phenomenon. And the increase of the stator stiffness will reduce the chaotic motion period.

Dynamics of simple earthquake model with time delay and variation of friction strength

We examine the dynamical behaviour of the phenomenological Burridge–Knopoff-like model with one and two blocks, where the friction term is supplemented by the time delay τ and the variable friction strength c. Time delay is assumed to reflect the initial quiescent period of the fault healing, considered to be a function of history of sliding. Friction strength parameter is proposed to mimic the impact of fault gouge thickness on the rock friction. For the single-block model, interplay of the introduced parameters c and τ is found to give rise to oscillation death, which corresponds to aseismic creeping along the fault. In the case of two blocks, the action of c1, c2, τ1 and τ1 may result in several effects. If both blocks exhibit oscillatory motion without the included time delay and frictional strength parameter, the model undergoes transition to quasiperiodic motion if only c1 and c2 are introduced. The same type of behaviour is observed when τ1 and τ2 are varied under the condition c1 = c2. However, if c1, and τ1 are fixed such that the given block would lie at the equilibrium while c2 and τ2 are varied, the (c2, τ2) domains supporting quasiperiodic motion are interspersed with multiple domains admitting the stationary solution. On the other hand, if (c1, τ1) warrant oscillatory behaviour of one block, under variation of c2 and τ2 the system's dynamics is predominantly quasiperiodic, with only small pockets of (c2, τ2) parameter space admitting the periodic motion or equilibrium state. For this setup, one may also find a transient chaos-like behaviour, a point corroborated by the positive value of the maximal Lyapunov exponent for the corresponding time series.

ANALYTICAL DESCRIPTION OF RECURRENCE PLOTS OF DYNAMICAL SYSTEMS WITH NONTRIVIAL RECURRENCES

In this paper we study recurrence plots (RPs) for the simplest example of nontrivial recurrences, namely in the case of a quasiperiodic motion. This case can be still studied analytically and constitutes a link between simple periodic and more complicated chaotic dynamics. Since we deal with nontrivial recurrences, the size of the neighborhood ∊ to which the trajectory must recur, is larger than zero. This leads to a nonzero width of the lines, which we determine analytically for both periodic and quasiperiodic motion. The understanding of such microscopic structures is important for choosing an appropriate threshold ∊ to analyze experimental data by means of RPs.