Free In-Plane Vibration of Super-Elliptical Plates | Zendy

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Free In-Plane Vibration of Super-Elliptical Plates

Author(s) -

Murat Altekin

Publication year - 2011

Publication title -

shock and vibration

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.418

H-Index - 45

eISSN - 1875-9203

pISSN - 1070-9622

DOI - 10.1155/2011/613521

Subject(s) - rectangle , ellipse , vibration , ritz method , lagrange multiplier , plane (geometry) , geometry , point (geometry) , vibration of plates , boundary value problem , boundary (topology) , mathematics , structural engineering , mathematical analysis , physics , engineering , acoustics , mathematical optimization

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.

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