Microstructure-dependent Band Gaps for Elastic Wave Propagation in a Periodic Microbeam Structure

Abstract

A new model for producing band gaps for flexural elastic wave propagation in a periodic microbeam structure is developed using an extended transfer matrix method and a non-classical Bernoulli–Euler beam model that incorporates the strain gradient, couple stress and velocity gradient effects. The band gaps predicted by the new model depend on the three microstructure-dependent material parameters of each constituent material, the beam thickness, the unit cell length and the volume fraction. A parametric study is conducted to quantitatively illustrate these factors. The numerical results reveal that the first band gap frequency range increases with the increases of the three microstructure-dependent material parameters, respectively. In addition, the band gap size predicted by the current model is always larger than that predicted by the classical model, and the difference is large for very thin beams. Furthermore, both the unit cell length and volume fraction have significant effects on the band gap.