By applying non-local elasticity theory and plane wave expansion (PWE) method to Timoshenko beam, the calculation method of band structure of a non-local piezoelectric phononic crystal (PC) Timoshenko nanobeam is proposed and formulized. In order to investigate the properties of wave propagating in the nanobeam in detail, bandgaps of first four orders are picked, and the corresponding influence rules of thermo-electro-mechanical coupling fields, non-local effect and geometric parameters on bandgaps are studied. During the research works, temperature variation, external electrical voltage and axial force are chosen as the influencing parameters related to the thermo-electro-mechanical coupling fields. Scale coefficient is chosen as the influencing parameter corresponding to non-local effect. Length ratio between materials PZT-4 and epoxy and height-width ratio are chosen as the influencing parameters of geometric parameters. Moreover, all the band structures and influence rules of Timoshenko nanobeam are compared to those of Euler nanobeam. The results are expected to be of help for the design of micro and nanodevices based on piezoelectric periodic nanobeams.

通过将非局部弹性理论和平面波扩展（PWE）方法应用于蒂莫申科梁，提出并提出了非局部压电声子晶体（Timoshenko）纳米束的能带结构计算方法。为了详细研究纳米束中波的传播特性，选取了前四个阶的带隙，研究了热电-机械耦合场，非局域效应和几何参数对带隙的影响规律。在研究工作中，选择温度变化，外部电压和轴向力作为与热电机械耦合场有关的影响参数。选择比例系数作为与非局部效应相对应的影响参数。选择材料PZT-4与环氧树脂的长径比和高宽比作为几何参数的影响参数。此外，将Timoshenko纳米束的所有能带结构和影响规律与Euler纳米束进行了比较。预期结果将对基于压电周期纳米束的微米和纳米器件的设计有所帮助。