In this paper, some of the scenarios that can occur in the numerical nonlinear non-smooth response of a vibro-impact single-degree-of-freedom system, symmetrically constrained by deformable and dissipative bumpers, were identified and described. The different scenarios, obtained varying selected dimensionless parameters, were investigated identifying homogeneous frequency intervals, characterized by similar features in terms of number and types of limit cycles, and resorting to phase portraits, basins of attraction and Fourier spectra. Despite the relative simplicity of the model, which however takes into account impact, clearance and unilaterality of the constraints, decreasing the dimensionless gap ${\delta }_{\mathrm{0}},$ from ${\delta }_{\mathrm{0}}=1$ to ${\delta }_{\mathrm{0}}=0,$ gradually more complex and varied scenarios, characterized by different types of secondary resonances (with right or left hysteresis or of non-regular type), cascades in the low frequency range, periodic, quasi-periodic or chaotic solutions were observed. The occurrence of primary and secondary grazing was also highlighted.

在本文中，确定并描述了振动冲击单自由度系统在数值非线性非线性非平稳响应中受变形和耗散保险杠对称约束的一些情况。研究了获得不同选择的无量纲参数的不同场景，以识别均匀的频率间隔，在极限环的数量和类型方面具有相似的特征，并诉诸相像，吸引盆和傅立叶谱。尽管模型相对简单，但是考虑了约束的影响，间隙和单边性，缩小了无因次差距${\delta }_{\mathrm{0}}，$ 从 ${\delta }_{\mathrm{0}}=\mathrm{1个}$ 到 ${\delta }_{\mathrm{0}}=0，$逐渐变得更加复杂和多样化，其特征是次级谐振的类型不同（具有右或左磁滞或非常规类型），在低频范围内出现了级联，观察到了周期性，准周期或混沌解。还强调了一次和二次放牧的发生。