A new model for predicting band gaps for flexural elastic wave propagation
in a periodic composite plate structure is developed using a non-classical
Kirchhoff plate model that is based on a modified couple stress theory, a
surface elasticity theory and a two-parameter Winkler–Pasternak elastic
foundation model. The formulation is based on the plane wave expansion
method and Bloch’s theorem. The current non-classical model simultaneously
incorporates microstructure, surface energy and foundation effects, unlike
existing models. When the microstructure and surface energy effects are
both suppressed, the new model reduces to the classical elasticity-based
model. The band gaps predicted by the newly developed model vary with the
microstructure-dependent length scale parameters, the surface elastic constants, the
elastic foundation moduli, the unit cell size, and the volume fraction. The
numerical results reveal that the first band gap including the foundation effect is
always smaller than that without considering the foundation effect, and
the first foundation band gap size increases with the increase of the elastic
foundation moduli. Also, the first band gap predicted by the new non-classical
model is always larger than that predicted by the classical model, but the
difference is diminishing as the plate thickness increases. In addition, it is
found that the sizes of the first band gap and the first foundation band gap
decrease with the increase of the unit cell length at different length scales.
Furthermore, it is seen that the volume fraction has a significant effect on the
sizes of the first band gap and the first foundation band gap, and band gaps
can be tailored by adjusting the volume fraction as well as the constituent
properties.
