国家自然科学基金重点项目(10732020),国家自然科学基金资助项目(11072008, 11302187)
提出了一种改进的渐近摄动法,并用该方法研究了同时含平方项和立方项的两自由度非线性系统在1:3内共振情况下的非线性动力学行为.分别在平均方程和原方程的基础上得到了幅频响应曲线和分叉图,对比表明两种结果基本吻合.改进后的渐近摄动法比原有渐近摄动法更容易应用于1:3内共振情况.
A refined asymptotic perturbation method was proposed and used to investigate the nonlinear dynamical behavior of twodegreeoffreedom systems with quadratic and cubic nonlinear terms under one-to-three internal resonance. Based on the averaged equations and the original differential equations, the frequency response curves and bifurcation diagrams were obtained respectively. Different from the original asymptotic perturbation method, the effectiveness of the refined asymptotic perturbation method for one-to-three internal resonance cases was shown.
胡海良,张伟.两自由度非线性系统1:3内共振的渐近摄动分析[J].动力学与控制学报,2015,13(2):97~100; Hu Hailiang,,Zhang Wei. Asymptotic perturbation analysis of twodegreeoffreedom nonlinear systems under onetothree internal resonance[J]. Journal of Dynamics and Control,2015,13(2):97-100.
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