FINITE ELEMENT ANALYSIS OF THREE-DIMENSIONAL VIBRATIONS OF THICK CIRCULAR AND ANNULAR PLATES

Three-dimensional vibrations of thick circular and annular plates are analyzed by a finite element method which, with a properly assumed set of displacement field, is different from the traditional 3-D finite element analysis and is reduced to a sequence of 2-D analyses one for each circumferential wave number. The present approach has several unique features: (1) It can obtain vibration frequencies which are comparable to, or as accurate as, those by other three-dimensional approaches, whenever comparisons between them are possible, and yet the formulation of the present method is simpler and its application is straightforward. (2) Different simply supported boundary conditions can be exactly imposed with the present approach. The latter feature may be quite difficult, if not impossible, for other methods. In the present analysis, vibration frequencies of a circular and an annular plate under different combinations of boundary conditions, wave numbers and finite element meshes are calculated, vibration characteristics are examined, and some typical mode shapes are shown graphically. Then, the results of some example problems by the present method are compared to those available in the literature to show its validity and accuracy.