Dynamics of a rotor composed of a flexible beam attached to a slewing rigid hub is presented in the paper. Dynamics of the structure is studied for a slender beam model, based on extended Bernoulli–Euler theory, which takes into account a nonlinear curvature, coupled transversal and longitudinal oscillations and non-constant angular velocity of the hub. Moreover, to demonstrate a general case for dynamical boundary conditions, lumped mass fixed at the beam tip is added. The partial differential equations (PDEs) are derived from Hamilton principle of the least action. The analytical solutions of the PDEs are obtained by the multiple time scale method applied directly to PDEs. Forced vibrations around selected resonance zones are studied and the influence of beam rotation, preset angle, hub radius, tip mass is presented. Hardening and softening phenomena, respectively for the first and the second mode, are obtained for various angular velocity values.

中文翻译：

---

具有回转运动尖端质量的延伸梁的非线性振动

本文介绍了由连接到回转刚性轮毂的柔性梁组成的转子的动力学。基于扩展的伯努利-欧拉理论，研究了细长梁模型的结构动力学，该理论考虑了非线性曲率、耦合的横向和纵向振荡以及轮毂的非恒定角速度。此外，为了演示动态边界条件的一般情况，添加了固定在梁尖端的集中质量。偏微分方程 (PDE) 源自哈密顿最小作用原理。PDE 的解析解是通过直接应用于 PDE 的多时间尺度方法获得的。研究了选定共振区周围的受迫振动，并介绍了梁旋转、预设角度、轮毂半径、尖端质量的影响。