应用均匀化等效材料参数分析梯度点阵材料波动问题的可行性探讨

Feasibility investigation of the analysis of gradient matrix materials' wave characteristics by homogeneous effective material parameters

以功能梯度蜂窝结构为对象,研究梯度指数的变化对准静态分析方法适用范围的影响。首先,从单胞结构尺寸和材料构成两方面考虑,探讨构造材料宏观属性的梯度变化方法,建立功能梯度蜂窝材料计算模型。然后,运用渐近均匀化方法,计算模型的宏观等效力学参数,并以这些静态参数为依据,计算材料的平均波速和波透射系数。接着,应用全位移场有限元方法,动态分析模型的波速和波透射系数,比较静态和动态的仿真结果,研究表明当梯度指数在一定范围内时,由准静态方法计算的动态参数与动态分析结果之间的误差不超过5%。最后,为进一步验证应用准静态方法预测梯度材料波动特性的适用条件,设计3种梯度蜂窝材料模型,采用准静态和动态2种方法,分别计算弹性波沿不同方向传播的波速。

Functional gradient honeycomb materials are taken as examples to investigate the impact of gradient index of materials on the errors of the gradient material dynamic parameters, which are calculated by using the quasi-static analysis method. Firstly, a design method targeted for gradient macroscopic properties of honeycomb materials is investigated by changing the material composition or the structure size in the unit cells, and a large amount of datum tables and curve figures are presented. Secondly, on the basis of these data, the computing models of gradient honeycomb materials are constructed, and the macro effective me- chanical parameters of the materials are evaluated by applying the asymptotic homogenization method, then according to these ef- fective material parameters, the mean velocity and the transmission coefficient of the elastic wave propagating in a slab of gradient honeycomb materials is solved. Furthermore, the mean velocity and the transmission coefficient are compared with the resulted data obtained by means of the full displacement field analysis with FEM. The comparative study results show that the errors be- tween the dynamic material parameters predicted by quasi-static analysis method and those gotten by the full field dynamic analy- sis method do not exceed 5% if the gradient index of gradient matrix materials belongs to a certain range. Finally, three examples of gradient honeycomb materials are constructed, and their dynamic material parameters in different directions are analyzed by using the quasi-static analysis method and the full field dynamic analysis method, separately. The numerical results further verify that it is feasible to analyze the wave characteristics of gradient matrix materials by quasi-static analysis method under the application condition of the gradient index of materials.