基于EFG法的可伸缩梁结构动力学分析

Dynamic Analysis of an Axially Deploying or Retracting Flexible Beam Based on the EFG Method

传统有限元法在处理时变边界、时变系数的轴向可伸缩梁时需要不断改变单元尺寸或单元数目,不利于程序化且计算精度无法保证。基于广义移动最小二乘(GMLS),采用不受单元限制的全域插值EFG法对柔性梁的变形场进行空间离散,根据哈密尔顿变分原理得到轴向可伸缩梁横向振动的无单元动力学离散方程;采用数值算例分析可伸缩梁的横向振动频率、各种轴向运动规律下梁末端的自由振动响应以及强迫振动响应。结果表明:全域插值EFG法可用于时变参数结构的动力学分析。

Dealing with the time-varying parameter system of an axially deploying or retracting flexible beam in the traditional FEM, it is necessary to change the element size and numbers constantly, which is not suitable for programming and cannot ensure the computational accuracy. Based on the generalized moving least squares （GMLS）, an improved global interpolating element-free Galerkin（EFG） method is applied to dynamics analysis of an axially deploying or retracting flexible beam. The element-free transverse vibration equations are built according to the Hamilton principle. The frequency characteristics, free vibration with different axially motion and the forced vibration response of the beam are calculated in numerical examples. By comparing with the reported available results, the feasibility of the EFG method applied for the time-varying parameter systems is verified.