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Dual flexible structural beam collision bifurcation motion and control
Author: LiuJiaBin
Tutor: LongXinHua
School: Shanghai Jiaotong University
Course: Mechanical Design and Theory
Keywords: Non- smooth systems Flexible structure VIBRO Branch Stability Chaos Control
CLC: TB122
Type: Master's thesis
Year: 2012
Downloads: 25
Quote: 0
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Abstract
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Various types of non-smooth dynamical systems in the prevalence of actual production as well as its impact on the production of an important role , has aroused a lot of attention and gain a lot of research and analysis. This article is mainly based on the coupling of a flexible structural beam collision model for collisions such non- smooth nonlinear systems were studied and analyzed . Firstly, based on the generalized Hamilton principle to establish a mass with a flexible cantilever end model , combined with Newton elastic collision , collision theory has been double cantilever beam model . Based on this model , combined with numerical simulations and experiments, analyzed the harmonic external excitation force hereinafter double cantilever beam collision response parameters obtained k = p / l -type cycle collision sports , bifurcation and chaotic motion ; while taking advantage of non- continuous mapping global Jacobian matrix theory to determine the stability of the system and obtained Lyapunov exponents . Subsequently, further analysis of the system parameters ( clearance , damping and nonlinear terms ) on the response of the system , and found that the gap caused by the Hopf bifurcation , jumping nonlinearities caused by nonlinear phenomena . Based on normalized linear simplified collision system model, we analytically cycle single collision system solutions , analyzes k = 1/1 Existence and different than the natural frequency of the system k = 1/1 Global Stability , and obtained k = 1/1 dual solution is unstable triangle area and period doubling bifurcation boundary curves . Finally, the use of energy-based control method and the improved OGY method, the chaos caused by the collision control and analysis carried out . Through numerical simulation analysis method is based on energy control area under constant control parameters control effect and good robustness ; while improved OGY also well suited for non-smooth system crash , the system is fast convergence the target unstable periodic orbits (Targeted UPO).
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