Free flexural vibration of honeycomb sandwich plate with negative Poisson's ratio simply supported on opposite edges

Honeycomb sandwich plate with negative Poisson's ratio is a special composite structure, whose dynamic behavior has not yet been studied. We applied Reddy's shear plate theory to do a free flexural vibration analysis of honeycomb sandwich plate with negative Poisson's ratio simply supported on opposite edges. Honeycomb core that consists of concave hexagon cellular element can be taken as an orthotropic layer. Equivalent elastic parameters of core were derived from the revised Gibson formula. From concrete example, we conclude that the classical sandwich plate theory and one order shear plate theory were not applicable to the vibration analysis of honeycomb sandwich plate. With Reddy's shear plate theory, we studied the influence of plate thickness of honeycomb sandwich plate, core plate, and angle of cellular element on flexural vibration frequency. Besides the above, a related curve chart was drawn. Results show that for honeycomb sandwich plate with negative Poisson's ratio simply supported on opposite edges, the natural frequency parameter increases with the ratio of plate thickness if ratio of plate thickness is less than a certain value. However, if the ratio of plate thickness was more than this value, the increase of natural frequency parameter behaves a complex variation with the increase of ratio of plate thickness. The conclusion derived from this paper provides a theoretical ground and numerical reference for the design and practical application of honeycomb sandwich plate.