In this paper we carry out an in-depth experimental and numerical investigation of a vibro-impact rig with a two-sided constraint and an external excitation given by a rectangular waveform. The rig, presenting forward and backward drifts, consists of an inner vibrating shaft intermittently impacting with its holding frame. Our interests focus on the multistability and the bifurcation structure observed in the system under two different contacting surfaces. For this purpose, we propose a mathematical model describing the rig dynamics and perform a detailed bifurcation analysis via path-following methods for nonsmooth dynamical systems, using the continuation platform COCO. Our study shows that multistability is produced by the interplay between two fold bifurcations, which give rise to hysteresis in the system. The investigation also reveals the presence of period-doubling bifurcations of limit cycles, which in turn are responsible for the creation of period-2 solutions for which the rig reverses its direction of progression. Furthermore, our study considers a two-parameter bifurcation analysis focusing on directional control, using the period of external excitation and the duty cycle of the rectangular waveform as the main control parameters.

在本文中，我们对具有双向约束和矩形波形给出的外部激励的振动冲击装置进行了深入的实验和数值研究。该钻机具有向前和向后的漂移，由一个内部振动轴组成，该振动轴间歇地撞击其保持架。我们的兴趣集中在系统在两个不同的接触表面下观察到的多重稳定性和分叉结构。为此，我们提出了一个描述钻机动力学的数学模型，并使用连续平台COCO，通过路径跟踪方法对非光滑动力系统进行了详细的分叉分析。我们的研究表明，多重稳定性是由两个折叠分叉之间的相互作用产生的，从而引起系统中的滞后现象。调查还揭示了极限周期的倍周期分叉的存在，而极限周期反过来又导致了第二阶段解决方案的创建，为此钻机将其前进方向反转了。此外，我们的研究考虑了以定向控制为重点的两参数分叉分析，该分析采用外部激励的周期和矩形波形的占空比作为主要控制参数。