摘要
基于SD振子,建立了非对称型SD振子模型及其运动方程。利用等价替换法与代入法求解8次方程,分析平衡点,研究该系统的分岔现象。运用平均法求其幅频方程,并利用Matlab等软件对该模型进行数值模拟,得到幅频响应曲线、系统的分岔图、相图和Poincare截面。结果显示,该系统具有与SD振子不相同的丰富非线性动力学特性,拓展了SD振子的研究和应用范围。
Based on SD oscillator, a new model of asymmetrical SD oscillator and its equation of motion are founded.Using the equivalence replacing method and substitution method to solve an eight times algebraic equa-tion, the equilibria are analyzed to study the bifurcation of this system.The amplitude-frequency equations are obtained by the average method,and the numerical simulation is used to obtain the amplitude-frequency curve, the bifurcation diagram of the system, the phase diagrams and Poincare sections.The results show the system has rich nonlinear dynamic behaviors, which are different from an SD oscillator and will enrich the range of SD oscil-lator in research and application.
出处
《石家庄铁道大学学报（自然科学版）》
2015年第1期101-105,共5页
Journal of Shijiazhuang Tiedao University(Natural Science Edition)
基金
国家自然科学基金项目(11372196)
河北省自然科学基金项目(A2014210104)
关键词
非对称型SD振子
分岔
幅频曲线
混沌
asymmetric SD oscillator
bifurcation
amplitude-frequency curve
chaos
