无理式系统的主共振分岔分析

Bifurcations of resonance in an irrational system

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α,当α>0时,其为正刚度系统;当α<0时,其为负刚度系统;当α=0时,其为线性系统。当α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。

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 α0,the nonlinear stiffness of the system was positive;when α0,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.