分段光滑碰撞振动系统吸引域结构变化机理研究

Structure change mechanism of the attractor basin in a piecewise-smooth vibro-impact system

在研究振动问题或利用振动时效技术消除工件应力时,常需要借助激振器或振动台等激振装置使物体产生振动。针对含间隙及预紧弹簧激振系统,建立了动力学模型,得到其解的解析表达式,利用胞映射法在不同Poincaré截面上获得系统中共存的吸引子及吸引域,分析了由鞍结分岔、周期倍化分叉及边界碰撞分岔诱导出现的吸引子共存情况,及由边界激变、吸引域边界质变及内部激变等全局分岔所引起的吸引子湮灭情况。研究表明由擦边分岔所诱导产生的平常型鞍点分支,及由周期倍化分岔所诱导产生的的翻转型鞍点分支的出现是造成系统出现分形吸引域边界的原因。

When the stresses of workpieces are eliminated by vibratory stress relief,it is often necessary to make objects vibrate by means of exciters or vibrators.The global dynamics of a kind of vibro-impact system with clearance and preloaded spring was devoted.The coexistence of attractors induced by saddle-node bifurcation,period-doubling bifurcation and boundary-collision bifurcation was focused.The attractor annihilation caused by boundary crisis,basin-boundary metamorphoses,and interior crises was also considered.The cell-to-cell mappings in different Poincarésections were employed to study the co-existence of attractors and their basins of attraction.The results show that the boundaries of basins of attraction are becoming fractal along with the appearance of the regular saddle points induced by grazing bifurcation and the flipped saddle points induced by period-doubling bifurcation.