A new dynamic model of shrouded blades with elastic support and variable cross-section is derived based on the Timoshenko beam theory, in which factors to be considered include centrifugal stiffening, spin softening, Coriolis force, blade stagger angle, and twist angle. The proposed model (PM) is verified by comparing the dynamic frequency results of the finite element model (FEM) and the PM. An impact-friction model of shrouded blades is established which can take into account the inertia effects of two passive blades. By comparing the vibration response of the two models (PM and FEM), the established impact-friction model is verified. Finally, the influences of normal contact stiffness, blade root support stiffness, and shroud position on the vibration response of the system are analyzed. Meanwhile, bifurcation diagrams, time-domain waveforms, phase diagrams, Poincaré maps, and frequency spectrum are utilized to analyze the nonlinear vibration characteristics of shrouded blades. The results show that the impact and friction between adjacent shrouds will cause the complex nonlinear vibration of the blades. Under small initial gaps, hard nonlinear phenomena can be observed in the vibration response of the shrouded blade. While under small initial preloads, it shows an obvious soft nonlinear phenomenon. Furthermore, with the increase of normal contact stiffness and blade root support stiffness, the resonance peak of the blade-tip flexural displacement decreases. When the shroud is closer to the blade-tip of the blade, the vibration reduction effect of the shrouded blade is better. The active blade experiences the chaos, period-one motion due to the nonlinear behavior of the impact-friction coupling at the adjacent shroud contact interfaces.

基于Timoshenko梁理论，推导了具有弹性支撑和可变横截面的带罩叶片的新动力学模型，其中要考虑的因素包括离心刚度，自旋软化，科里奥利力，叶片错位角和扭曲角。通过比较有限元模型（FEM）和PM的动态频率结果，验证了所提出的模型（PM）。建立了带罩叶片的冲击摩擦模型，该模型可以考虑两个被动叶片的惯性效应。通过比较两个模型（PM和FEM）的振动响应，验证了建立的冲击摩擦模型。最后，分析了法向接触刚度，叶片根部支撑刚度和护罩位置对系统振动响应的影响。同时，分叉图，时域波形，相图，庞加莱图和频谱用于分析带罩叶片的非线性振动特性。结果表明，相邻罩之间的冲击和摩擦将导致叶片复杂的非线性振动。在较小的初始间隙下，可以在带罩叶片的振动响应中观察到坚硬的非线性现象。在较小的初始预紧力下，它表现出明显的软非线性现象。此外，随着法向接触刚度和叶片根部支撑刚度的增加，叶片尖端弯曲位移的共振峰减小。当罩靠近叶片的叶片尖端时，罩的叶片的减振效果更好。主动的刀片会遇到混乱，