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Complex Dynamical Behavior Research in a Class of Nonlinear Moving Belt Systems

Author: ZuoYuLong
Tutor: LiQunHong
School: Guangxi University
Course: Applied Mathematics
Keywords: nonlinear moving belt sliding bifurcation Filippov system periodic motion
CLC: O19
Type: Master's thesis
Year: 2013
Downloads: 49
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Abstract


The moving belt system is a typical class of piecewise smooth dynamic systems, and it has a widely range of applications in mechanical systems. The dynamic behavior of the moving belt system is very complicated due to the oscillators on the moving belt which might exhibit three different states of motion:stick, slip, or stick-slip. Therefore, the study of the moving belt system is one of the important research directions of nonlinear dynamics, and it has drawn extensive attention of scholars at home and abroad. This thesis studies dynamical behavior of a class of nonlinear moving belt systems, and the main research contents and research results are as follows:(1) For a single-degree-of-freedom nonlinear moving belt dynamical system, based on the analytical research of the sliding region and the equilibrium of the moving belt system, one-or two-parameter continuation of several types of periodic orbits, for example sliding orbit, crossing-sliding orbit, crossing-crossing orbit, and grazing orbit, are calculated using the speed of moving belt and friction amplitude as the bifurcation parameters. Codimension-1sliding bifurcation curves, codimension-2sliding bifurcation points and global bifurcation diagram in parameter space of the system are obtained.(2)For a two-degree-of-freedom nonlinear moving belt dynamical system, the boundary conditions and sliding fields of the system on different switching manifolds and the admissible equilibrium of the system are discussed. Using the speed of moving belt and friction amplitude as the bifurcation parameter respectively, the dynamical behavior of the oscillator is studied by construction the Poincare maps, and the relationship between the two oscillators motion are also discussed. The research results show that the dynamical behavior of nonlinear moving belt system includes not only fold bifurcation, period-doubling bifurcation leading to chaos, but also sliding bifurcation, the phenomenon that periodic motion and chaos appeared alternately, which are the unique dynamical behavior of non-smooth dynamical systems.

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