【摘要】 研究了一类滞后非线性系统在多频激励下的超谐共振和亚谐共振。利用平均法得到了系统的超谐共振和亚谐共振的一次近似解,并且研究了各种参数对近似解的幅频曲线的影响,发现超谐共振幅频曲线转折点出现鞍结分岔,而亚谐共振的幅频曲线为叉形分岔。研究结果为工程中这一类系统的分析和控制提供了理论依据。更多还原

【Abstract】 In this paper the super-harmonic and sub-harmonic resonance of the hysteretic nonlinear system with three-frequency excitation are investigated. Through Averaging Method,the first-order approximate solution is obtained.And the effects of all kinds of parameters on the curve of the frequency-amplitude are also studied. The results show that saddle-node bifurcation arises in the turning points of the curve of the super-harmonic frequency-response, while the curve of the sub-harmonic frequency-response is pitch-fork bifurcation. This method is useful to analyze and/or control the similar systems in engineering.更多还原