Asymptotic analysis for resonance cycle solution of a type of strongly nonlinear systems
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摘要:
强非线性系统经引入参数变换,并在一定的假设条件下,可转化为弱非线性系统,将其解展成为改进的傅立叶级数后,利用参数待定法可方便地求出强非线性系统的共振周期解.研究了Duffing方程的主共振、Van der Pol方程的3次超谐共振和Van der Pol-Mathieu方程的1/2亚谐共振周期解.这些例子表明近似解与数值解非常吻合.
Abstract:
Based on a certain hypothesis,the strongly nonlinear system was transformed into a weakly nonlinear system by introducing a parameter transformation.Its solutions were expanded into the improved Fourier series,and the resonance cycle solutions were conveniently obtained by the undetermined parameter method.Using the method,we studied the principal resonance cycle solutions of the Duffing equation,the 3 ultraharmonic resonance cycle solutions of the Van der Pol-Mathieu equation.The examples showed that the approximate solutions closely coincided with numerical solutions.
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彭献,陈自力.一类强非线性系统共振周期解的渐近分析[J].动力学与控制学报,2004,2(1):46~50; Peng Xian, Chen Zili. Asymptotic analysis for resonance cycle solution of a type of strongly nonlinear systems[J]. Journal of Dynamics and Control,2004,2(1):46-50.
