Wind and Structures, An International Journal, cilt.24, sa.4, ss.307-331, 2017 (SCI-Expanded)
Free transverse vibration of shear deformable
super-elliptical plates with uniform thickness was studied based on Mindlin
plate theory using finite element method. Quadrilateral isoparametric elements
were used in the paper. Sensitivity analysis was made to determine the
influence of thickness, aspect ratio, and the shape of the plate on the natural
frequency. Accuracy of the results computed in current study was validated by
comparing them with the solutions available in the literature. The results
reveal that frequencies of clamped super-eeliptical plates lie in the range
bounded by elliptical and rectangular plates irrespective of the aspect ratio,
and furthermore, the frequency decreases if the super-elliptical power increases.
A similar trend was observed for simply supported plates with high aspect
ratio. The free vibration response for the first and the second
symmetric-antisymmetric (SA) modes were found to be different for high aspect
ratio. The results reveal that using insufficient number of degrees of freedom
results in finding a totally different relation between the super-elliptical
power and the frequency.