点阵板结构固有频率等效模型误差分析

Error Analysis of Equivalent Model of Natural Frequency of Lattice Plate Structure

点阵材料是一种新兴的轻质高强的材料,由于其具有多尺度特征,采用离散模型需要对所有板杆进行建模和网格划分,导致频率分析费时。常采用均匀化后的等效模型进行分析。主要对等效模型进行频率分析,讨论点阵材料各参数对频率的影响。以一块四边固支的仅具有面内周期性的点阵板为研究对象,分别使用离散模型和三维周期性材料均匀化等效模型、周期性板结构的均匀化等效模型,开展周期性点阵板结构的固有频率的计算,分别改变点阵板的单胞内部参数、单胞的排布个数、单胞的构型,讨论这些因素对固有频率的影响。进而,以离散模型的结果为基准,对等效模型的求解结果进行误差分析,结果显示针对具有面内周期性的点阵板结构,Mindlin等效板模型预测的固有频率误差较小。

Lattice material is a new kind of lightweight and high-strength material.Due to its multi-scale characteristics,it is time-consuming to conduct frequency analysis using discrete finite element model,which models and meshes all the plates and rods.The homogenized equivalent model is often used for analysis.The frequency of the equivalent model was mainly analyzed and the influence of the parameters of the lattice material on the frequency was discussed.Taking a lattice plate clamped at four edges with only in-plane periodicity as an example,the natural frequency of the periodic lattice plate structure was calculated using the discrete model,the three-dimensional periodic material homogenization equivalent model and the periodic plate structure homogenization equivalent model.By changing the internal parameters of the unit cell,the arrangement of the unit cell and the cell configuration respectively,the effects on the results were discussed.Then,based on the results of the discrete model,the error analysis of the solution results of the equivalent model was carried out.The results show that for the lattice plate structure with in-plane periodicity,the error of the natural frequency predicted by the Mindlin equivalent plate model is small.