Vibration of thick auxetic plates

• As a plate's Poisson's ratio becomes more negative, the Mindlin-to-Kirchhoff natural frequency ratio increases with diminishing rate.
• Simplifying assumptions such as constant shear correction factor and exclusion of rotary inertia is valid for plates with positive Poisson's ratio.
• The assumptions of constant shear correction factor and no rotary inertia for auxetic plates give overestimated natural frequency.
• For obtaining the natural frequency of auxetic plates, the shear correction factor must allow the variation of Poisson's ratio and the rotary inertia must be included.

This short communication investigates the effect of negative Poisson's ratio on the natural frequency of thick plates of arbitrary shape. Using the Mindlin plate theory, it was generally found that as the plate's Poisson's ratio becomes more negative, the Mindlin-to-Kirchhoff natural frequency ratio increases with decreasing rate. Upon comparing (a) the use of the simplified constant shear correction factor and the more accurate variable shear correction factor, (b) with and without rotary inertia, it was found that all the four combinations stated in (a) and (b) do not give appreciable difference when the Poisson's ratio of the plate is positive. However in the case of plates with negative Poisson's ratio, results reveal that when at least one of the simplifying assumptions is used, the Mindlin-to-Kirchhoff natural frequency ratio is overestimated, and that the overestimation further increases when both the simplifying assumptions are used. When benchmarked against Reddy plate theory, the use of variable shear correction factor has almost the same effect as the inclusion of rotary inertia. Hence the use of either variable shear correction factor or rotary inertia is proposed for modeling the vibrational frequencies of conventional and auxetic isotropic plates.

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