Theoretical characteristics of the vibration of sandwich plates with in-plane negative poisson's ratio values

This paper is concerned with re-entrant cell honeycombs which show in-plane negative Poisson's ratio values, in which their anisotropic mechanical properties are described using the cellular material theory. Out-of-plane shear moduli are affected by the unit cell geometric parameters and, for some ranges of the latter, it is possible to obtain higher values of the shear moduli compared to those of a regular hexagonal honeycomb, in particular for cell geometries with a negative Poisson's ratio. A first order sandwich plate theory is applied in order to obtain the fundamental frequencies of sandwich laminates in cylindrical bending and for the simply supported case. Sensitivities of the frequencies per unit mass versus the geometric cell paramcters are also calculated. The results suggest that the dynamic performance of a sandwich structure could be significantly improved with a proper design of the unit cell shape of the honeycomb. In particular, re-entrant cell cores offer improvements in bending stiffness capabilities for particular cell parameter ranges.