复合材料变截面旋转薄壁悬臂梁自由振动分析  

FREE VIBRATION ANALYSIS OF ROTATING COMPOSITE THIN-WALLED CANTILEVER BEAMS WITH VARIABLE CLOSED-SECTION

作　　者：马静敏[1] 任勇生[2] 姚文莉[3] 

机构地区：[1]山东科技大学理学院,山东青岛266510 [2]山东科技大学机械电子工程学院,山东青岛266510 [3]青岛理工大学理学院,山东青岛266510

出　　处：《工程力学》2013年第1期37-44,63,共9页Engineering Mechanics

基　　金：国家自然科学基金项目(10972124);山东省教育厅科技计划项目(J08LB04);山东科技大学春蕾计划项目(06540040921)

摘　　要：基于拉格朗日方程推导出复合材料封闭变截面旋转薄壁梁的自由振动方程。与基于哈密顿原理的动力学建模方法相比,该文所采用的方法更为简洁。此外,在薄壁梁的结构模型中还考虑除横向剪切外的扭转、拉伸和弯曲引起的翘曲,具有考虑翘曲因素多的特点。给出了两种刚度配置下的变矩形截面旋转悬臂直梁的自由振动方程简化形式及其相应的迦辽金法求解的固有频率。基于大型通用有限元软件ANSYS,计算了薄壁变截面旋转悬臂梁的固有频率,并且与迦辽金法的求解结果进行了对比。分析了复合材料的弹性耦合、铺层角度、截面变化和旋转速度对薄壁梁的自由振动的影响。The motion equations of rotating composite thin-walled cantilever beams with variable closed-section are derived based on Lagrange＇s equation. This dynamics modeling method is more concise than the one based on the Hamiltonian principle. And the dynamic model includes the warping effects of classical torsion-related warping and out-of-plane warping due to uniform axial extension and bending as well, but not includes transverse shear related warping. The simplified free vibration equations of two stiffness configuration taper rotating box beams are presented. And the corresponding solution is obtained by a Galerkin method. The finite element analysis sof~：ware ANSYS is used to calculate the natural frequency of the rotating beams. And the results are compared with the approximated solutions obtained by Galerkin method. The composite elastic coupling, ply angle, taper ratio and rotating speed influences on the free vibration frequencies are investigated.

关 键 词：复合材料 薄壁梁 固有频率 变截面 转速 ANSYS软件 

分 类 号：TB123[理学—工程力学]