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Averaging of a nonlinear bipolar model with phase transition and oscillating external forces

Medjo T. T.

Journal of Applied Analysis

2015

Vol. 21, nr 2

123--146

In this article, we consider a non-autonomous nonlinear bipolar with phase transition in a two-dimensional bounded domain. We assume that the external force is singularly oscillating and depends on a small parameter ε. We prove the existence of the uniform global attractor Aε. Furthermore, using the method of [9] in the case of the two-dimensional Navier-Stokes systems, we study the convergence of Aε as e goes to zero.

Dynamics of wheel-tyre subjected to moving oscillating force

Bogacz R., Kocjan M., Kurnik W.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

2002

Vol. 6, No 3

343-350

The subject of the paper is analysis of wheel of a moving railway vehicle which is subjected to a moving oscillating force. Rail ring is treated as a beam of small curvature connected to wheel axle with a Winkler foundation. Bernoulli-Euler and Timoshenko beam model is used. Results are gained using Fourier transformation. Space and space-time graphs, showing wave propagation in subcritical and supercritical zones of excitation, concerning resonance of transverse vibrations, are included.