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High-dimensional nonlinear dynamical systems and Bifurcation of dimensionality reduction methods

Author: ZhenYaXin
Tutor: ZhangChiPing
School: Harbin Institute of Technology
Course: Computational Mathematics
Keywords: Nonlinear Galerkin Method Dimensionality reduction Oil film force Sealing force Branch
CLC: O322
Type: Master's thesis
Year: 2008
Downloads: 82
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Abstract


In this paper, based on Chebyshev orthogonal polynomial theory and nonlinear Galerkin method for high-dimensional nonlinear dynamical system dimensionality reduction techniques and nonlinear oil film force , the sealing force of the rotor - bearing system of nonlinear dynamics . Complex dynamical systems often exhibit high-dimensional , nonlinear , strong coupling characteristics, the dynamics of such systems even with the numerical method there are many difficulties. Nonlinear dynamical behavior of non- autonomous system model is often the low-dimensional manifold dynamics are controlled , thus simplifying dimension reduction has become the phenomenon theoretically reveal the dynamics necessary step and prerequisite . In this paper, after translation theory Chebyshev orthogonal polynomials obtained by a linear term periodic changes over time nonlinear non- autonomous system Liapunov-Floquet transformation matrix , converts the linear time-invariant system entry , and then use the nonlinear Galerkin method to reduce the dimension to this system . Through the system before and after dimensionality reduction and time course of phase trajectory comparison chart , indicating dimensionality reduction success. Jeffcott rotor for single disc - bearing system , the establishment of its nonlinear oil film force and sealing force of the kinetic equation, where Capone used oil film made ??in 1991 under the assumption that the short- bearing nonlinear oil film force model, which model has a good accuracy and convergence , a sealing force with a nonlinear model Muszynska . In this paper, Runge - Kutta method to solve the nonlinear rotor - bearing dynamic system, the system has been periodic response and nonlinear dynamics , rendering the system using the maximum method with the rotor speed and the change in mass eccentricity of the disc bifurcation diagram . Speed ??changes in the studied range , by plotting the Poincare section map, plots, phase diagrams , etc., found that as the rotor speed and the quality of the eccentric disc changes , phylogenetic periodic motion , bifurcations and quasi-periodic motion , and then enter chaotic state, and later into two periodic motion , and finally to the end of cycle sport .

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CLC: > Mathematical sciences and chemical > Mechanics > Vibration theory > Nonlinear vibration
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