Synchronization Properties in Coupled Dry Friction Oscillators

作者: Michał Marszal , Andrzej Stefański

DOI: 10.1007/978-3-319-71243-7_4

关键词: Synchronization (computer science)TopologyMaster stability functionLine (geometry)VibrationPhysicsSpring (device)Representation (mathematics)Toy modelNumerical integration

摘要: Self-excited vibrations in friction oscillators are known as stick-slip phenomenon. The non-linearity the force characteristics introduces instability to steady frictional sliding. self-excited oscillator consists of mass pushed horizontally on surface, elastic element (spring) and a drive (convey or belt). Described system serves classic toy model for representation motion. Synchronization is an interdisciplinary phenomenon can be defined correlation time at least two different processes. This chapter focuses synchronization thresholds networks with dry coupled by linear springs. Oscillators connected nearest neighbour fashion into topologies open closed ring. In course numerical modelling we interested identification complete cluster regions. determined numerically using brute integration means master stability function (MSF). Estimation MSF conducted approach called two-oscillator probe. Moreover, perform parameter study two-dimensional space, where configurations explored. results indicate that applied non-smooth such oscillator. occur line one obtained numerically.

参考文章(65)
K Popp, N Hinrichs, M Oestreich, Dynamical behaviour of a friction oscillator with simultaneous self and external excitation Sadhana-academy Proceedings in Engineering Sciences. ,vol. 20, pp. 627- 654 ,(1995) , 10.1007/BF02823210
J. WARMIŃSKI, G. LITAK, M.P. CARTMELL, R. KHANIN, M. WIERCIGROCH, APPROXIMATE ANALYTICAL SOLUTIONS FOR PRIMARY CHATTER IN THE NON-LINEAR METAL CUTTING MODEL Journal of Sound and Vibration. ,vol. 259, pp. 917- 933 ,(2003) , 10.1006/JSVI.2002.5129
Vladimir N. Belykh, Igor V. Belykh, Erik Mosekilde, Cluster synchronization modes in an ensemble of coupled chaotic oscillators. Physical Review E. ,vol. 63, pp. 036216- 036216 ,(2001) , 10.1103/PHYSREVE.63.036216
Steven H. Strogatz, Allan McRobie, Edward Ott, Bruno Eckhardt, Daniel M. Abrams, Theoretical mechanics: crowd synchrony on the Millennium Bridge. Nature. ,vol. 438, pp. 43- 44 ,(2005) , 10.1038/43843A
D. P. Hess, A. Soom, Friction at a Lubricated Line Contact Operating at Oscillating Sliding Velocities Journal of Tribology-transactions of The Asme. ,vol. 112, pp. 147- 152 ,(1990) , 10.1115/1.2920220
Mauricio Barahona, Louis M. Pecora, Synchronization in small-world systems. Physical Review Letters. ,vol. 89, pp. 054101- ,(2002) , 10.1103/PHYSREVLETT.89.054101
Andrzej Stefański, Jerzy Wojewoda, Marian Wiercigroch, Tomasz Kapitaniak, None, Chaos caused by non-reversible dry friction Chaos Solitons & Fractals. ,vol. 16, pp. 661- 664 ,(2003) , 10.1016/S0960-0779(02)00451-4
Arthur T. Winfree, Biological rhythms and the behavior of populations of coupled oscillators Journal of Theoretical Biology. ,vol. 16, pp. 15- 42 ,(1967) , 10.1016/0022-5193(67)90051-3