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Dynamic characteristics of a mechanical impact oscillator with a clearance
International Journal of Mechanical Sciences ( IF 7.3 ) Pub Date : 2020-07-01 , DOI: 10.1016/j.ijmecsci.2020.105605
Xiaohong Lyu , Quanfu Gao , Guanwei Luo

Abstract A two-degree-of-freedom mechanical impact oscillator with a clearance is considered. Pattern types, occurrence and stability domains and bifurcation characteristics of periodic motions are investigated through two-parameter co-simulation analysis. With varying of the bifurcation parameters in two directions, forward and backward, two-parameter grazing, period-doubling and saddle-node bifurcations of impactless, fundamental and subharmonic motions are calculated and analyzed. There exist two types of transition zones, hysteresis and liguliform zones, in mutual transition between neighboring motions p/1 and (p + 1)/1 (p ≥ 0). Dynamics in the hysteresis and liguliform zones is introduced in detail. Attracting domains and Poincare mapping diagrams of coexisting motions in the neighborhood of grazing bifurcations are discussed. Pattern types and bifurcations of subharmonic motions in liguliform zones show regularity. In the two-parameter plane, two grazing bifurcation curves of p/1 (p ≥ 0) motion and period-doubling and saddle-node bifurcation curves of (np + 1)/n (n ≥ 1) motion intersect at a singular point along the upper boundary of liguliform zones LZp/1∩(p + 1)/1. Consequently, the singular point is a point of double-grazing bifurcation of p/1 motion and codimension-2 flip-fold bifurcation of (np + 1)/n motion. The grazing bifurcation of neighboring motions is continuous and reversible only at the singular points, and displacement amplitudes of the impact oscillator vary continuously when the varying parameter passes through the grazing bifurcation boundary.

中文翻译:

带间隙机械冲击振荡器的动态特性

摘要 考虑一种带间隙的二自由度机械冲击振荡器。通过双参数联合仿真分析,研究了周期运动的模式类型、发生域和稳定域以及分岔特征。随着前向和后向两个方向的分岔参数的变化,计算和分析了无碰撞、基波和次谐波运动的双参数掠过、倍周期和鞍点分岔。在相邻运动p/1和(p+1)/1(p≥0)之间的相互过渡中存在两种类型的过渡区,滞后区和舌状区。详细介绍了滞后区和舌状区的动力学。讨论了掠食分岔附近共存运动的吸引域和庞加莱映射图。舌状区次谐波运动的模式类型和分叉显示出规律性。在双参数平面上,两条p/1(p≥0)运动的掠分岔曲线和(np+1)/n(n≥1)运动的倍周期和鞍点分岔曲线相交于一个奇异点沿叶状区 LZp/1∩(p+1)/1 的上边界。因此,奇异点是 p/1 运动的双掠分叉点和 (np + 1)/n 运动的 codimension-2 翻转分叉点。相邻运动的掠分岔仅在奇异点处是连续可逆的,当变化的参数通过掠分岔边界时,冲击振子的位移幅度连续变化。两条p/1(p≥0)运动的掠分岔曲线和(np+1)/n(n≥1)运动的倍周期和鞍节点分岔曲线在沿舌状带上边界的奇异点处相交LZp/1∩(p+1)/1。因此,奇异点是 p/1 运动的双掠分叉点和 (np + 1)/n 运动的 codimension-2 翻转分叉点。相邻运动的掠分岔仅在奇异点处是连续可逆的,当变化的参数通过掠分岔边界时,冲击振子的位移幅度连续变化。两条p/1(p≥0)运动的掠分岔曲线和(np+1)/n(n≥1)运动的倍周期和鞍结分岔曲线在沿舌状带上边界的奇异点处相交LZp/1∩(p+1)/1。因此,奇异点是 p/1 运动的双掠分叉点和 (np + 1)/n 运动的 codimension-2 翻转分叉点。相邻运动的掠分岔仅在奇异点处是连续可逆的,当变化的参数通过掠分岔边界时,冲击振子的位移幅度连续变化。因此,奇异点是 p/1 运动的双掠分叉点和 (np + 1)/n 运动的 codimension-2 翻转分叉点。相邻运动的掠分岔仅在奇异点处是连续可逆的,当变化的参数通过掠分岔边界时,冲击振子的位移幅度连续变化。因此,奇异点是 p/1 运动的双掠分叉点和 (np + 1)/n 运动的 codimension-2 翻转分叉点。相邻运动的掠分岔仅在奇异点处是连续可逆的,当变化的参数通过掠分岔边界时,冲击振子的位移幅度连续变化。
更新日期:2020-07-01
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