无理式系统的主共振分岔分析

研究了一类无理式系统的主共振分岔。该系统为一连杆系统模型，其动力学行为取决于光滑参数 ，当 时，其为正刚度系统；当 时，其为负刚度系统；当 时，其为线性系统。当 逐渐增加时，系统从弱非线性系统变成强非线性系统。研究结果表明，无理式系统的性质和多项式系统的性质是不同的。最后采用奇异性理论分析了共振解的演化过程

Bifurcations of resonance in an irrational system

Here,bifurcations of resonance in an irrational system were studied.The system was derived from a linkage mechanism and its dynamic behavior was dependent on the smooth parameter α.When α>0,the nonlinear stiffness of the system was positive;when α<0,it was negative;when α=0,the system is linear.When |α| increased gradually,the system changed from a weakly nonlinear system to a strongly nonlinear one.The study results showed that the properties of the irrational system are different from those of a polynomial system.Finally,the evolution process of the resonance solution to the system was studied by employing singularity theory.