基于变长度单元ANCF的轴向伸展悬臂梁振动分析

伸展悬臂梁系统中含有刚体运动和大变形运动，属于时变刚柔耦合非线性动力学问题。采用Shabana提出的绝对节点坐标法（ANCF），建立了一种变长度的Euler-Bernoulli梁单元模型。从大变形条件下准确的曲率和Green- Lagrangian正应变出发，基于考虑惯性力的虚功原理，得到了轴向伸展悬臂梁的单元非线性动力学方程组，以及组装后的伸展悬臂梁系统的非线性动力学方程组。最后，通过算例分析了材料特性参数（弹性模量、密度）和伸展规律（匀速伸展、匀加速伸展）对伸展悬臂梁系统的末端非线性挠度响应的影响。
Abstract：A deploying cantilever beam system has rigid body motion and large deformation motion, so its vibration problem is time-varying and rigid-flexible coupled nonlinear dynamic one.Here, the absolute node coordinates formulation (ANCF) proposed by Shabana was adopted to establish a length-varying Euler-Bernoulli beam element model.Starting from the accurate curvature under the condition of large deformation and Green-Lagrangian normal strain, based on the virtual work principle considering inertia force, nonlinear dynamic equations of a beam element, and those of a deploying cantilever beam system after element-assembling were derived.Finally, the effects of material characteristic parameters including elastic modulus and mass density and deploying laws including constant speed deploying and constant acceleration one on nonlinear deflection response at free end of the deploying cantilever beam system were analyzed through numerical examples.