旋转几何非线性复合材料薄壁梁的自由振动分析

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

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。

A rotating composite thin-walled beam is a class of typical structure used in study on vibration control of advanced helicopter blades and wind turbine blades.The dynamic behavior investigation of this structure is of significance in theory and practice.However,so far the dynamic behavior study on the above-mentioned structure is limited only for rotating composite beams with small elastic deformation.The free vibration of a rotating composite thin-walled beam with large deformation was studied here.The governing nonlinear equations of motion for the rotating composite thin-walled beam were derived using Hamilton＇s energy principle and the variational-asymptotical method（VAM） on the basis of von Karman＇s assumption.The nonlinear free vibration of the beam was studied using Galerkin method and the harmonic balance method.The large amplitude of free vibration of the beam could be expressed as a nonlinear eigenvalue problem and solved using an iterative solution procedure.Numerical results were obtained for a laminated composite configuration thin-walled beam with circumferentially uniform stiffness（CUS）.The results showed the effect of fiber orientation and rotating speed on the relation between nonlinear natural frequency and amplitude.The developed model could be capable of describing nonlinear free vibration behaviors of a rotating composite thin-walled beam with large deformation.