点阵多孔金属夹芯板振动特性分析及优化设计

VIBRATION CHARACTERISTICS AND OPTIMIZATION OF TRUSS-CORED METAL SANDWICH PLATES

采用空间桁架结构分析的网架结构连续化方法对点阵多孔金属夹芯板的夹芯层桁架进行了连续化处理,即,将夹芯层桁架等效为连续介质,并分别推导了金字塔型、四面体型、kagome型和4杆型点阵多孔金属夹芯板的抗弯刚度和等效剪切刚度.然后,应用分解刚度法推导了四边简支条件下点阵多孔金属夹芯板的固有振动频率公式,并与有限元计算结果进行了对比,表明所得公式具有较高的精度.最后,研究了夹芯板单胞结构尺寸对固有振动频率的影响,以夹芯层高度和桁架杆截面尺寸为设计变量,以第一阶频率最大化为目标对夹芯板进行了优化,优化后的夹芯板振动频率得到了明显提高.

The space grid homogenization theory used in space grids design was adopted to homogenize the trusscored metal sandwich plates. The bending stiffness and equivalent shear stiffness of the homogenized plates were obtained by using Reissner sandwich theory and the space grid homogenization method respectively. The formulae of the natural frequencies of four typical truss-cored metal sandwich plates were. then derived by using the Method of Split Rigidities （MSR）. The frequencies of truss-cored metal sandwich plates obtained by the formulae are in good agreement with those by finite element method. Moreover, the influence of structure parameter of the unit cell on the natural frequencies was analyzed. Optimization with the goal of a maximal first natural frequency was performed by optimizing the height of truss core and the cross-sectional area of the truss. The truss-cored metal sandwich plates after optimization have a much higher first frequency compared with the original design.