论文信息 - Synchronization of self-excited oscillators suspended on elastic structure

Synchronization of self-excited oscillators suspended on elastic structure

We consider the dynamics of self-excited oscillators suspended on the elastic structure. We show that for the given conditions of the structure, initially uncorrelated oscillations of each oscillator can synchronize, i.e., all oscillators evolve periodically with the frequency of the oscillations of elastic structure. Basing on the theory of linear oscillations we introduced the mechanism responsible for the observed synchronization. We argue that the observed phenomena are generic in the parameter space and independent of the number of oscillators and their location on the elastic structure.

[1] J. E. Littlewood,et al. On Non‐Linear Differential Equations of the Second Order: I. the Equation y¨ − k(1‐y2)y˙ + y = bλk cos(λl + α), k Large , 1945 .

[2] N. Levinson,et al. A Second Order Differential Equation with Singular Solutions , 1949 .

[3] S. Boccaletti,et al. Synchronization of chaotic systems , 2001 .

[4] Parlitz,et al. Period-doubling cascades and devil's staircases of the driven van der Pol oscillator. , 1987, Physical review. A, General physics.

[5] M. Rabinovich,et al. Stochastic synchronization of oscillation in dissipative systems , 1986 .

[6] Carroll,et al. Synchronization in chaotic systems. , 1990, Physical review letters.

[7] Chaos synchronization and riddled basins in two coupled one-dimensional maps , 1998 .

[8] Tomasz Kapitaniak,et al. On transverse stability of synchronized chaotic attractors , 1996 .

[9] A. Shabana. Theory of vibration , 1991 .

[10] H. Fujisaka,et al. Stability Theory of Synchronized Motion in Coupled-Oscillator Systems. II: The Mapping Approach , 1983 .

[11] J. Grasman. Relaxation oscillations of a van der pol equation with large critical forcing term : (preprint) , 1978 .

[12] Tomasz Kapitaniak,et al. Synchronization of mechanical systems driven by chaotic or random excitation , 2003 .