【摘要】 针对起重机箱形伸缩臂在轴向周期载荷作用下的动力稳定性和传统两结点梁单元在结构分析中精度不够的问题,依据有限元插值理论采用五次Hermite插值,构造考虑二阶效应的非线性三结点Euler-Bernoulli梁单元横向位移场,推导出新型三结点梁单元的单元矩阵.运用Lagrange方程建立周期载荷作用下伸缩臂在小变形情况下的参数振动方程,给出了起重机伸缩臂的动力不稳定区域边界,并讨论阻尼对伸缩臂动力稳定性的影响.分析结果表明,非线性三结点梁单元与传统两结点梁单元划分3～4个单元具有相同的计算精度,应用有限单元法求解动力稳定问题是有效的;随着阻尼系数的增大,伸缩臂动力不稳定区域逐渐减小,阻尼的存在有利于伸缩臂的动力稳定性.更多还原

【Abstract】 In order to study the dynamic stability of crane’s telescopic booms under periodic load,and examine the poor accuracy of the traditional two-node beam element in structural analysis,this paper proposes to implement the quintic Hermite interpolation to establish the transverse displacement field of non-linear 3-node Euler-Bernoulli beam element,that considers the second-order effect,thus developing matrixes of 3-node beam element.The parametric vibration equation of stepped columns with small deformation under periodic load was established by the Lagrange equation;the dynamic instability region of telescopic booms was obtained,and then the effect of damping on the dynamic stability of telescopic booms was discussed.The results of the analysis indicate that the non-linear 3-node beam element has the same accuracy as traditional 2-node beam element dividing into 3 to 4 elements.By utilizing the finite element method to analyze the dynamic stability,it is shown effective;even more,the dynamic instability region reduces as the damping coefficient increases,which means damping is advantageous to the structural dynamic stability.更多还原