Study On Dimension Reduction Of Nonlinear Muti-Degrees-Offreedom System With Multiple Parameters

The dimension reduction process for large complex structures in modern engineering is an important issue in nonlinear dynamics, and the usual dimension reduction methods have its own limitations. Moreover in the manufacturing process of the large-scale structures and machines design and physical parameters of a system, including geometrical and material and the effect of various parameters on the dynamic performance of the system must be taken into consideration. Therefore, the search for an effective dimensional reduction method to reduce high-dimensional complex nonlinear system to a low-dimensional system with only a few degrees-of-freedom such that the dynamical behaviors of stability which can be easily investigated by modern bifurcation and chaos theory is an important topic in nonlinear dynamics currently.The problem of dimension reduction of nonlinear systems with multiple parameters is addressed in terms of structural characteristics of the system in this paper. The dimension reduction approach based on the fixed interface component mode synthesis of substructures is employed to analyze the system, and then an order reduction for the entire nonlinear system is proposed along with the process of sensitivity analysis. First the system is divided into a number of subsystems according to the characteristics of practical structure, some of which are linear subsystem, and the remains are nonlinear. Then the frequencies and modes related to parameters of the linear subsystems are derived from the sensitivity analysis theory. Finally lower dimension nonlinear dynamic systems with multiple parameters are obtained by synthesizing the nonlinear subsystems and the modes truncated from the linear subsystems in terms of the fixed interface mode synthesis.For a specific example, amplitude-frequency characteristic curves for both the lower dimension nonlinear dynamic system obtained here and the original nonlinear system are presented respectively. By comparison, the dynamic behaviors exhibited in both the reduced and the original nonlinear systems are qualitatively the same within error permitted. So the dimension reduction deduced in this paper can not only effectively reduce the dimension of original nonlinear system but also improve the computation efficiency.