We consider two cantilevered beams undergoing frictional impacts at the free end. The beams are designed to be of similar geometry so that they have distinct but close natural frequencies. Under harmonic base excitation near the primary resonance with the higher-frequency fundamental bending mode, the system shows a strongly modulated non-periodic response. The purpose of this work is to analyze to what extent the non-periodic vibro-impact dynamics can be predicted. To this end, we use a recently developed modeling and simulation approach. The approach relies on component mode synthesis, the massless boundary concept and an appropriate time stepping scheme. Unilateral contact and dry friction are modeled as set-valued laws and imposed locally within the spatially resolved contact area. A linear model updating is carried out based on the natural frequencies and damping ratios identified in the regime without impacts. The nonlinear simulation of the steady-state response to forward and backward stepped sine excitation is compared against measurements. The results are in very good agreement, especially in the light of the uncertainty associated with the observed material loss in the contact region and the nonlinear behavior of the clamping.

我们考虑两个悬臂梁在自由端受到摩擦冲击。梁被设计成具有相似的几何形状，因此它们具有不同但接近的固有频率。在具有较高频率基本弯曲模式的初级谐振附近的谐波基础激励下，系统显示出强调制的非周期性响应。这项工作的目的是分析可以在多大程度上预测非周期性振动冲击动力学。为此，我们使用了最近开发的建模和仿真方法。该方法依赖于分量模式合成、无质量边界概念和适当的时间步长方案。单边接触和干摩擦被建模为定值定律，并在空间分辨的接触区域内局部施加。基于在没有影响的情况下确定的自然频率和阻尼比进行线性模型更新。将正向和反向步进正弦激励的稳态响应的非线性模拟与测量值进行比较。结果非常一致，特别是考虑到与接触区域中观察到的材料损失和夹持的非线性行为相关的不确定性。