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). Key words: locally resonant piezoelectric/elastic phononic crystal double-layer nanobeam; nonlocal piezoelectricity theory; plane wave expansion method; symmetric and antisymmetric modes; nano electro-mechanical system I. INTRODUCTION Recently, different kinds of NEMS have been widely applied to national defense, civil use, biomedicine and so on, which have excellent characteristics such as small size, superhigh frequency, lower power, high sensitivity and so on. The existing piezoelectric nano devices include biological motor, resonant sensor, filter and so on [1] . As for artificial periodic composite structures, PCs in various forms have attracted wide attentions on account of the existing of band gaps, which have been applied to vibration and noise control, acoustics lens, acoustical devices and so on [2] . Generally, PCs can be divided to Bragg scattering and LR types. Particularly, the opening of band gaps of LR PCs is mainly based on the locally resonance of scatters, which have an advantage in opening band gaps in low frequency region [3] . With the rapid development of industry, double-layer structures with the multifunctional characteristics, such as light weight, large stiffnes, good impact resistance and so on, have been widely used in the field of naval architecture, aeronautics, astronautics, civil engineering and so on [4] . Moreover, the cavity of a double-layer structure in engineering is generally periodically added sandwich to enhance structural performance, which makes the double-layer structures have an excellent convergence point with PCs [5] . Hence, based on the common application background in acoustical devices of NEMS and PCs, excellent characteristics of piezoelectric nanostructures, PCs and double-layer structures w...
