复合材料封闭变截面薄壁梁自由振动分析

摘要

基于拉格朗日方程建立了复合材料封闭变截面薄壁梁的自由振动微分方程,给出了两种刚度配置下的变矩形截面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,铺层角度和截面变化对薄壁梁的自由振动的影响.%The equations of motion for the free vibration of composite thin-wall variable closed cross-section beams were derived based on Lagrange' s equation of the second kind. Two taper box beams with different stiffness distribution were taken into account and their corresponding simplified forms of the free vibration equations were presented and solved by means of Galerkin method. The finite element analysis software, ANSYS was used to calculate the natural frequencies of the composite thin-walled cantilever beams. The results were compared with Galerkin solutions. The influences of composite elastic coupling, ply angle and taper ratio on thin-walled beams' free vibration were investigated.