No abstract

Free axisymmetric vibrations of annular stepped plates have been studied on the basis of the classical theory of plates. Applying the uniform plate solution to each zone of different thickness; considering the continuity and boundary conditions l yielda a system of eight equations. Frequency determinants of such plates,with different step radii, are derived for various combinations of boundary conditions. Consequently the values of the resonant frequencies of the first two symmetric modes are calculated. Different graphs are included to facilitate the use of this material for design purpose. • 7 • 1 KEYWORDS Transvers vibrationi annular plates9 stepped circular plates,boundary conditions,natural frequency issymmetric model.

The finite element method is applied to the free transverse vibration of circular plate. The assumptions of the classical plate theory are app_ lied in deriving the basic equations required for the solution of the problem. The triangular bending element used in describing the bending of the plate is characterized with only nine degrees of freedom. Consequently the transverse deformation of the element is expressed by a polynomial interpolation function of third order.

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 conditions in order to obtain the solution of such plates.