| (3)在通带频率范围内，由于准周期结构自身的结构特点，波动会发生局部化。在带隙频率范围内，两种模型的PZT-4/Epoxy/CoFe2O4 Fibonacci准周期结构中弹性波的衰减程度均比相应的理想周期结构的衰减程度小。这与Pb/Epoxy纯弹性Fibonacci准周期结构的局部化特性相一致。
附录A
准周期结构能量平衡关系式(22)的推导：
左半空间 ,入射SV波的速度和应力场为：
 (A.1)
在结构的最左边界面 入射波的应力和速度场为：
 (A.2)
根据参考文献[18]，入射波在单位时间内的瞬时功率（能流密度）为：
 (A.3)
则入射波在一个周期内携带的平均能流为
 (A.4)
据此相同的推导过程，可以得到界面的反射波和 界面的透射波在一个周期内携带的平均能流分别为
 (A.5)
 (A.6)
能量反射系数和能量透射系数分别定义为反射波和透射波各自所携带的能量占入射波能量的比例来表示，即 和 。由能量守恒，可以得到
 (A.7)
此式即为准周期结构的能量所满足的平衡关系，可以用来验证数值结果的正确性。
附录B
式(22)的理论证明：
 (B.1)
 (B.2)
上两式中上标“ ”代表复共轭。化简(B.1)与(B.2)之和可以得到
 (B.3)
在式(B.1),(B.2)和(B.3)的化简中均利用了准周期结构全局转换矩阵的性质 .
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