标题:
最简规范形的计算及其应用Computation of the Simplest Normal Form and Its Application
作者:
陈淑萍
关键字:
功能梯度材料, 规范形, 稳定性, 非线性变换Functionally Graded Materials, Normal Form, Stability, Nonlinear Transformations
期刊名称:
《Dynamical Systems and Control》, Vol.5 No.3, 2016-07-18
摘要:
本文提出了计算四维非线性系统最简规范形的新方法，得到了计算四维非线性系统最简规范形的通用公式，并将该方法用于计算受横向和面内载荷共同作用的功能梯度材料矩形板系统的平均方程。理论结果表明，功能梯度材料矩形板系统在区域I内是稳定的，最后，利用四阶Rung-Kutta算法对功能梯度材料矩形板系统的稳定性行为进行数值模拟。
This paper presents a new computation method for obtaining a significant refinement of the sim-plest normal form for four dimensional nonlinear systems. The formulae are derived, which can be used to compute the coefficients of the simplest normal form and the associated nonlinear transformation. By using the simplest normal form theory, the stability analysis of a simply-sup- ported functionally graded materials (FGMs) rectangular plate subject to the transversal and in- plane excitations is investigated. It is seen that the stability is exhibited under certain circum-stances. The fourth-order Runge-Kutta algorithm is utilized to do numerical simulation of the sta-bility behavior of the FGM rectangular plate.