Nonlinear Dynamical Analysis Of High-Dimensional Systems With Parametric Excitation

There are almost many kinds of nonlinear factors in the real dynamical systems in engineering, such as: clearance, dry friction, bearing oil film in the mechanical systems and the constitutive relations of the nonlinear composite materials. If these nonlinear factors are neglected, it will sometimes cause the unacceptable error in analyse and calculation. Especially to the dynamical problems with the long times courses of the systems, even neglect very weak nonlinear factors, it often cause the essential error in analyse and calculation. To these problems, they were only solved correctly by depend on the theory of nonlinear oscillations. Now nonlinear dynamical systems with parametric excitation are one of the most important systems in the theory of nonlinear oscillations. There are more abundant and complicated phenomena in nonlinear dynamical systems with parametric excitation, such as bifurcations and chaos. It needs more than one degree to describe the characteristic of the real dynamical systems in engineering. So it is very important to research the higher dimensional nonlinear dynamical systems with parametric excitation.In this dissertation we study the system with parametric excitation for the rectangular composite laminated plates with reinforced anti-symmetrically and symmetrically cross-by fiber and the torsional vibration system of crankshafts with variable inertia, research the nonlinear dynamical systems with parametric excitation, use the numerical simulation to analyse the periodic value, bifurcations and chaos of the systems. The main research work and conclusions are summaries as follows:1. Introduce the mechanical character of the composite material. Considering the nonlinear factors like material, damp, geometry, a two-degree-of-freedom nonlinear dynamic equations are deduced respectively for composite laminated plates with reinforced anti-symmetrically and symmetrically cross-by fiber and use numerical simulation method to analyse bifurcations and chaos of the system, point that the route of the system entering into chaotic regime and analyse the influence of the direction of cross-by to the dynamic character of the composite laminated plate.2. Introduce the researching of torsional vibration system of crankshafts. Base on the lumped parameter model of the torsional vibration system of crankshafts with variable inertia and considering the nonlinear elasticity force and nonlinear dissipative force, a six-degree-of-freedom nonlinear dynamical equations with parametric excitation and compulsive force are deduced. Use numerical simulation method to simulate the multi-parametric combination resonance condition for the system, analyse the periodic value, bifurcations and chaos of the system.