Wave propagation in a non-local piezoelectric phononic crystal Timoshenko nanobeam

Abstract

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.