【摘要】 对一类采用半主动控制的非线性系统进行了解析研究。利用平均法得到了该系统在主共振情况下的一阶近似解,并通过奇异性理论在系统的激励幅值和频率调谐量构成的参数空间中对分岔模式进行了分类,表明系统的响应为双翼尖点分岔的普适开折。研究结果证明,该方法不但可以分析半主动控制系统的动力响应,还可以得到该系统的各种分岔行为,从而可用于这一类半主动控制非线性系统的动态分析和控制。更多还原

【Abstract】 This paper focuses on a nonlinear system under semi-active control. At first the first-order approximate solution to the main resonance is obtained by the averaging method. And then the bifurcation modes are classified in the parametric space composed of the amplitude of excitation and the modulation factor based on the singularity theory. It is shown that the response is the universal unfolding of the winged cusp bifurcation. It is shown that the method presented here could be used to analyze the dynamic response of this kind of semi-active control system and obtain all the bifurcation curves. This provides an efficient method that could be used to analyze and control the dynamic behaviours of this kind of semi-active nonlinear system.更多还原