Bandgaps in phononic crystal third-order shear deformation microbeams

Periodic composite beams play an important role in the bandgap design of phononic crystals. However, for thick beams or high frequencies, conventional theoretical displacement assumptions for beams have limitations. Therefore, it is desirable to improve the accuracy of the vibration frequencies and bandgaps of phononic crystals by using higher-order beam theory. In this work, a modified couple stress theory accounting for the microstructure effect is combined with the third-order shear deformation beam theory to quantitatively study bandgaps in phononic crystal microbeams under different thicknesses and geometric parameters. The elastic wave band structure of the phononic crystal beams is calculated using an improved plane wave expansion method and compared numerically with the finite element model. In addition, compared with the Bernoulli–Euler and Timoshenko beams, the current third-order shear beam has better prediction accuracy for the first bandgap. The numerical results also show that the microstructure effect is significant at the micron scale. Furthermore, at all length scales, the bandgap sizes change significantly with the change in unit cell length and volume ratio.