旋转几何非线性复合材料薄壁梁的自由振动分析

研究具有几何非线性的旋转复合材料薄壁梁的自由振动。梁的变形引入了Von Kármán几何非线性， 基于Hamilton原理和变分渐进法 (Variational-Asymptotical Method -VMA)，导出旋转复合材料薄壁梁的非线性振动偏微分方程组。采用Galerkin法将振动方程离散化为常微分方程组。借助于谐波平衡法 (Harmonic Balance Method -HBM) 建立自由振动的振幅-非线性固有频率关系方程。将上述方程化为非线性特征值问题，采用迭代算法进行求解。将所建立的旋转复合材料薄壁梁非线性自由振动分析模型和计算方法，应用于周向均匀刚度配置(Circumferentially Uniform Stiffness –CUS) 构型复合材料薄壁梁，通过数值计算揭示了纤维铺层角、旋转速度对非线性振动固有频率-振幅关系的影响。

Free vibration of rotating composite thin-walled beam with large deformation

Rotating composite thin-walled beam is a class of typical structure which is using in study of vibration control of advanced helicopter blades and wind turbine blades. The dynamic behavior investigation of these structures has significance in theory and practice. However, so far dynamic study on the above-mentioned structures is limited only the rotating composite beams with small elastic deformations. The free vibration of the rotating composite thin-walled beams undergoing large deformations is studied in the paper. The nonlinear governing equations of motion for the rotating composite thin-walled beam are derived using Hamilton’s energy principle and variational-asymptotical method (VAM) on the basis of von Karman’s assumption. The nonlinear vibration of the beam is studied using Galerkin method and harmonic balance method. The large amplitude free vibration of the beam can be expressed as a nonlinear eigenvalue problem and solved using an iterative solution procedure. Numerical results are obtained for Circumferentially Uniform Stiffness (CUS )laminated composite configuration thin-walled beam. The study exhibit the effect of the fiber orientation and rotating speed on nonlinear natural frequency vs. amplitude curves. The developed model can be capable of describing nonlinear free vibration behaviors of rotating composite thin-walled beam with large deformations. The present work extends the previous analysis done for linear vibration model of non-rotating composite thin-walled beam.