Theoretical and numerical modeling of membrane and bending elastic wave propagation in honeycomb thin layers and sandwiches

Abstract

Elastic wave propagation in honeycomb thin layers and sandwiches is investigated theoretically and numerically by using the Bloch wave transform, so the modeling of a unique primitive cell is sufficient to understand the wave propagation phenomena through the whole periodic structure. Both in-plane (with respect to the plane of the honeycomb layer) and out-of-plane waves are analyzed by developing finite element models formulated within the framework of the Mindlin–Reissner theory of plates. The dispersion relations and the phase and group velocities as function of frequency and of direction of propagation are calculated. The anisotropic behaviors and the dispersive characteristics of the studied periodic media with respect to the wave propagation are then analyzed. According to our numerical investigation, it is believed that the existence of bandgaps is probably not possible in the frequency domain considered in the present work. However, as an important and original result, the existence of the “backward-propagating” frequency bands, within which Bloch wave modes propagate backwards with a negative group velocity, is highlighted. As another important result, the comparison is made between the first Bloch wave modes and the membrane and bending/transverse shear wave modes of the classical equivalent homogenized orthotropic plate model of the honeycomb media. A good comparison is obtained for honeycomb thin layers while a more important difference is observed in the case of honeycomb sandwiches, for which the pertinence of finite element models is discussed. Finally, the important role played by the honeycomb core in the flexural dynamic behaviors of the honeycomb sandwiches is confirmed.