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中文摘要：
将功能梯度材料引入声子晶体之中,构成由均匀材料和功能梯度材料交替复合而成的材料常数宏观上呈连续变化的一维声子晶体结构.应用平面波展开法研究了该结构中存在的弹性波带隙特征,并得到前四阶归一化频率带隙结构随材料长度和功能梯度材料指数因子变化的关系图.通过对其带隙结构与不含功能梯度材料的常规声子晶体帯隙结构比较可知：功能梯度材料使原有带隙结构发生变化,含有功能梯度材料的声子晶体较常规声子晶体前两阶带隙归一化起始频率升高.这些结果扩宽了功能梯度材料的使用范围,提升了声子晶体工程可靠性,为含有功能梯度材料的声子晶体在工程实际中的应用提供了理论依据和指导.
英文摘要：
The propagation of elastic waves in one-dimensional phononic crystals（PCs） which are composed of both functionally graded materials（FGM） and isotropic material has been studied by using the plane wave expansion method.The material properties of FGM are varied according to a well-known rule,such as the exponential function.The influences of the exponential factor of FGM,filling fraction of two kinds of materials and length of materials on the first two-order normalized frequency gaps location and width are discussed,respectively.These results provide the theoretical basis and guidance for PCs with FGM widely used in engineering practice.
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