The dynamic behaviour of composites containing long soft fibers of elliptic cross section is studied in the frequency range where the material behaves as a metamaterial. The results of homogenization theory for composites containing soft inclusions are recalled, showing the conditions that lead to a frequency dependent dynamic density coming from the inner resonance of soft inclusions. The dynamic density is expressed from the resonance frequencies and participation factors of the inner inclusions obtained by solving a localization problem. The solution to this problem is obtained for a composite containing long fibers of elliptic cross section by using an expansion into Mathieu functions. The set of resonance frequencies and participation factors can be split into different subsets corresponding to the different symmetries of localization problems related to different directions of the macroscopic acceleration. All results are found to be consistent with the extreme cases of aspect ratios corresponding to stratified media (plane inclusions) and circular fibers.

在材料表现为超材料的频率范围内研究了包含椭圆形横截面的长软纤维的复合材料的动力学行为。回顾了包含软夹杂物的复合材料的均质化理论的结果，显示了导致频率依赖性动态密度来自软夹杂物内部共振的条件。动态密度由解决局部化问题而得到的内含物的共振频率和参与因子表示。通过使用扩展到Mathieu函数的方法，可以解决包含椭圆形横截面长纤维的复合材料的问题。共振频率和参与因子的集合可以被分为与对应于宏观加速度的不同方向的定位问题的不同对称性相对应的不同子集。发现所有结果与对应于分层介质（平面夹杂物）和圆形纤维的长宽比的极端情况一致。