Size effects on the band gap of flexural wave propagation in one-dimensional periodic micro-beams

The mechanical properties of micro-scale materials are different from their macroscopic counterparts. This study investigates the impact of the size effect on the band structure of a one-dimensional periodic microstructure. The equation of motion for the Euler-Bernoulli beam model considering the size effect is derived based on the modified coupled stress theory, and the transfer matrix method is employed to obtain the band structure considering the size effect. The results obtained with the modified couple stress theory are compared with those obtained using the classical theory. The size effect increases the flexural stiffness of the micro-beams, causing the band gap to move to a higher frequency. In addition, the effects of the material distribution and geometric period on the band gap are also investigated. It is found that the size effect, which has a significant effect on the band structure of the microstructure, cannot be neglected.