Free in-plane vibration of super-elliptical plates

Article type: Research Article

Authors: Altekin, Murat

Affiliations: Department of Civil Engineering, Yildiz Technical University, 34210 Esenler, Istanbul, Turkey. Tel.: +90 212 3835148; Fax: +90 212 3835133; E-mail: [email protected]

Abstract: Free in-plane vibration of super-elliptical plates of uniform thickness was investigated by the Ritz method. A large variety of plate shapes ranging from an ellipse to a rectangle were examined. Two cases were considered: (1) a completely free, and (2) a point-supported plate. The geometrical boundary conditions were satisfied by the Lagrange multipliers. The results were compared with those of rectangular plates. Basically good agreement was obtained. Matching results were reported, and the discrepancies were highlighted.

Keywords: Super-elliptical, plate, Ritz, in-plane, vibration

DOI: 10.3233/SAV-2010-0527

Journal: Shock and Vibration, vol. 18, no. 3, pp. 471-484, 2011