The paper proposed a model of a locally resonant (LR) piezoelectric/elastic phononic crystal (PC) nanobeam with periodically attached “spring-mass” resonator and additional spring between upper and lower nanobeams, as well as horizontal spring between mass and foundation. Euler beam theory and nonlocal piezoelectricity theory are coupled and introduced to plane wave expansion (PWE) method to calculate the band structures of such a model with different parameters. Numerical results and further analysis demonstrate that all the bands of double-layer nanobeam can be divided into symmetric and antisymmetric ones. Adding additional and horizontal springs play a role in control the symmetric and antisymmetric bands respectively, which make wider band gaps be opened than corresponding single-layer nanobeam. Moreover, the change of parameters of electro-mechanical coupling fields and resonator can be applied to effectively control the starting frequencies and widths of band gaps, which can provide a theoretical basis for active control of vibration. Effects of geometric and non-dimensional nonlocal parameters on band gaps are also discussed. All the studies are expected to be applied to actively control vibration propagation in the field of nano electro-mechanical system (NEMS).

该论文提出了一种局部谐振 (LR) 压电/弹性声子晶体 (PC) 纳米梁模型，该纳米梁具有周期性连接的“弹簧质量”谐振器和上下纳米梁之间的附加弹簧，以及质量和基础之间的水平弹簧。将欧拉梁理论和非局域压电理论耦合并引入平面波展开 (PWE) 方法，以计算具有不同参数的此类模型的能带结构。数值结果和进一步的分析表明，双层纳米束的所有波段都可以分为对称和反对称波段。添加额外的和水平的弹簧分别起到控制对称和反对称带的作用，这使得比相应的单层纳米束打开更宽的带隙。而且，改变机电耦合场和谐振腔的参数可以有效控制带隙的起始频率和宽度，为振动的主动控制提供理论依据。还讨论了几何和无量纲非局部参数对带隙的影响。所有研究都有望应用于纳米机电系统（NEMS）领域的主动控制振动传播。