The Analysis Of Engineering Chaotic Vibration System And Its Computer Simulation

Chaotic vibration is a new discipline originated from the combination of chaos theory with mechanics.More and more scholars are absorbed in chaotic vibration because of its deep theoretical significance and wide application. However, since there are many difficulties in its application, products with respect to it are rare. Therefore, how to step up research of application of chaotic vibration becomes temporally urgent.Based on above background, a planar slider-crank mechanism with clearance, which is a typical engineering chaotic vibration system, and its dynamical response are selected and analyzed, in order to realize the combination of chaotic theory with engineering application and to serve latest theory as the guidance for structure design.The main contents are given in this paper as follows:Firstly, elementary concept and theory are introduced, including the definition of chaos and its characteristics, concept of phase space. During introducing chaos, several classical chaos examples are analyzed consisting of Lorenz attractor, Japanese attractor in continuous system, and Logistic equation in discrete system. While introducing phase space, forced Duffing equation and Logistic equation are taken as examples. Then, several description methods of chaos are discussed, including Poincare mapping, power spectrum, self-correlation and Lyapunov exponent whose definition and significance are given emphasis on. Furthermore, the status in present and development trend of dynamical research of mechanism with clearance and chaotic vibration are discussed.Secondly, the dynamical model of mechanism with clearances and its solution of motion differential equations are studied. Based on perturbation coordinate approach and Lagrange equation, adopting Dubowsky impact pair model, the planar slider-crank mechanism with two clearances simultaneously in pairs is modeled. Thus, responding differential equations are gotten. Because of highnonlinearity of equations, improved Gear method(stiffness method) is adopted to numerically simulation. The dynamical response and chaotic character of mechanism are discussed. Moreover, the effect of clearance in pair, crank speed and contact stiffness in joint on dynamical response are studied.Finally, chaotic control is discussed. The control method of chaotic vibration and its application are introduced. In the end, the advices of how to preserve chaotic vibration are proposed.