摘要
在正则摄动理论的基础上,引进了新的独立自变量,从而形成了一种研究非线性振动的新的解析近似方法——双时间变量正则摄动法。此方法尤其适用于多自由度非线性保守系统中内共振现象的讨论。利用它可以方便地求得振幅微分方程组的第一积分,进而定性定量地确定振幅随时间的变化以及由此所产生的各自由度之间的能量交流。作为应用举例,本文求解了处于内共振下的三自由度非线性系统,理论分析与数值计算结果获得了良好的吻合。
Based on the canonical perturbation theory, a second independent variable is defined beside the time t. This means a new approach to analytical solutions of nonlinear vibrations—the Canonical Double Variables Perturbation Method is developed in this paper. This method is especially effective for dealing with internal resonances in nonlinear conservative multidegree-of-freedom systems. The first integrals of the differential equations for the amplitudes can be found out conveniently. Further the amplitude beating with the time and therefore the exchange of energy between the concerned degrees of freedom can be determined qualitatively and quantitatively. As an application example, a three-degree-of-freedom system under internal resonance is investigated. The results of the theoretical research and numerical calculations agree with each other satisfactorily.
出处
《西安工业学院学报》
1992年第3期1-12,共12页
Journal of Xi'an Institute of Technology
关键词
非线性振动
时间参数
摄动法
non-linear system non-linear vibration time quantities canonical perturbation method resonance
