AXISYMMETRIC VIBRATION OF STEPPED CIRCULAR PLATES WITH ELASTICALLY BUILT-IN BOUNDARY CONDITION

Document Type : Original Article

Author

Assistant Professor, Dept. of Mechanical Design, Faculty of Eng. & Tech., Helwan University, Cairo,Egypt.

Abstract

This paper deals with the axisymmetric motion of stepped circular plates in which its boundary is considered elastically built -in. The solution of uniform plate is applied to each step of the plate. Continuity conditions at each step must be satisfied besides the boundary condit-ions in order to obtain the solution of such plates. The boundary of the plate is considered to be elastically built-in in a manner that prevents transverse edge motion and provides a restoring edge moment linearly related to edge rotation. Thus limiting cases are a clamped plate and a simply supported plate.
The eigenvalues of the axisymmetric modes are obtained by using a constructed computer program written with FORTRAN-IV language. The program is applied to circular plates of different step radii. At the same time two different forms of the plate are considered. Finally, a discussion of the results obtained is presented in order to show the effect of the fixity parameter ( proportionality factor between tne moment and slope of the plate at the boundary) on the values of the natural frequency of the plate at different step radii and different symmetric modes.

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