The nonlinear dynamics of a tip excited cantilevered beam with an end-mass attached to elastic-damping support is considered in this paper. This prototypical system is examined using a minimal two degree of freedom (DOF) model and its bifurcation characteristics, computed by AUTO software, is compared with the analytical solutions and that of the full system using multi-body dynamic simulation. The spring–damper support at tip introduces the length dependent geometric nonlinearities in the structure. Consequently, the two-to-one internal resonance between the first lateral mode and the first vertical mode is imposed. When the excitation frequency is in the vicinity of the first vertical natural frequency (or twice the first lateral natural frequency), lateral response loses its stability after a certain force threshold. It is found (a) the minimal model is adequate to understand the first bifurcation (pitchfork) and the subsequent Hopf bifurcation and (b) the threshold force can be tuned by changing the initial length of the support elements.

本文考虑了末端激励附接到弹性阻尼支架上的末端激励悬臂梁的非线性动力学特性。使用最小二自由度（DOF）模型检查该原型系统，并将其分叉特性（由AUTO软件计算）与解析解进行比较，并使用多体动态仿真对整个系统进行分析。尖端的弹簧阻尼器支架在结构中引入了长度相关的几何非线性。因此，在第一横向模式和第一垂直模式之间施加了一对二的内部共振。当激励频率在第一垂直固有频率附近（或两倍于第一横向固有频率）时，在一定的力阈值之后，横向响应会失去稳定性。