Free transverse vibration of shear deformable super-elliptical plates


Creative Commons License

Altekin M.

Wind and Structures, An International Journal, vol.24, no.4, pp.307-331, 2017 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 24 Issue: 4
  • Publication Date: 2017
  • Doi Number: 10.12989/was.2017.24.4.307
  • Title of Journal : Wind and Structures, An International Journal
  • Page Numbers: pp.307-331
  • Keywords: plate, vibration, frequency, Mindlin, finite element, THICK RECTANGULAR-PLATES, RAYLEIGH-RITZ METHOD, NATURAL FREQUENCIES, 3-DIMENSIONAL VIBRATION, BENDING ANALYSIS, ORTHOGONAL POLYNOMIALS, CIRCULAR PLATES, ANNULAR PLATES, VARIABLE THICKNESS, FINITE-ELEMENT

Abstract

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.