Journal of Sound and < ibration (2000) 230(1), 45 } 67 doi:10.1006/jsvi.1999.2600, available online at http://www.idealibrary.com on THEORETICAL CHARACTERISTICS OF THE VIBRATION OF SANDWICH PLATES WITH IN-PLANE NEGATIVE PO ISSO N ’S R ATIO VALUES F. SCARPA AND G. TOMLINSON Dynamics Research Group, Department of Mechanical Engineering, ;niversity of She.eld, She.eld S13JD, England (Received 4 January 1999, and in ,nal form 21 June 1999) 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 a!ected 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 "rst 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 parameters are also calculated. The results suggest that the dynamic performance of a sandwich structure could be signi"cantly improved with a proper design of the unit cell shape of the honeycomb. In particular, re-entrant cell cores o!er improvements in bending sti!ness capabilities for particular cell parameter ranges.  2000 Academic Press 1. INTRODUCTION When a sample of material is stretched it is naturally expected that a contraction in the direction perpendicular to the stretching one will occur. The expectation arises from the fact that all naturally occurring materials appear to exhibit this property. The Poisson ratio is the quantity de"ning this fundamental material feature. For an isotropic material the Poisson ratio is de"ned by " !    , (1) where   is the tensile strain in the stretching direction and   the tensile strain perpendicular to this. Since most materials contract in the perpendicular direction to the applied load the presence of a minus sign in the de"nition ensures a positive value of the ratio. On the contrary, a material with a negative Poisson's ratio expands in all directions when pulled in only one, leading to an increase of its volume. Evans [1] was the "rst to de"ne such materials as auxetic, from the Greek 0022-460X/00/060045#23 $35.00/0  2000 Academic Press