Chaotic dynamics of simple vibrational systems

Nonlinear transient and chaotic interactions in disc brake squeal

“…14(b) using delay embedding [32]. The two-dimensional POINCARE section is fractal and shows a very similar attractor to the original three-dimensional attractor, thus indicating self-similarity [37]. Further reducing the POINCARE section into LORENZ cross sections [32] is avoided for the following reasons: (1) the computational time needed increases significantly 3 ; and (2) for each projection, a loss of accuracy of approximately one order of magnitude will degrade the quality of the fractal map generated [32].…”

Numerical Simulation and Mechanism Study of Two Level Partial Blocks Vibration Motor

“…Consequently, the system produces motion with a wide power spectrum curve and some irregular performance, such as large vibrating amplitude, great vibrating force, high vibrating intensity and other special inertia properties. It is very significant to overcome some of the work barriers and solve some critical technologies or bottlenecks of the development of the vibrating machines, especially as the large, medium and super large vibrating mill, vibrating screen, vibrating mixer, vibrating conveyor and so on [7] . Conclusions 1.…”

The dynamic behavior of a cantilever beam coupled to a non-ideal unbalanced motor through numerical and experimental analysis

“…Verichev et al [15] studied a similar system consisting of a rotor motor coupled to a four degree-of-freedom system. Using an averaging method, the system is reduced, near the main resonance range, to the Lorenz system with four parameters defined in a three-dimensional Cartesian phase space.…”