V. Sonzogni

Transverse vibrations of an isotropic, simply supported rectangular plate with an orthotropic inclusion

An approximate analytical solution is obtained for the title problem by using a Navier-type solution. It is shown that the fundamental frequency coefficient obtained by means of this procedure is in reasonably good agreement with the result obtained by using a finite element algorithmic methodology. Obviously the type of material disturbance considered introduces considerable change in the dynamic behavior of the structural element and this fact is clearly shown in the variation of the fundamental frequency value.

Buckling of circular, annular plates of non-uniform thickness

Abstract This paper deals with the solution of the title problem in the case where the outer boundary is subjected to uniform, hydrostatic pressure while the inner edge of the plate is free. It is assumed that the plate thickness varies (a) in a discontinuous fashion and (b) linearly. An approximate approach is proposed using polynomial coordinate functions which identically satisfy the boundary conditions at the outer edge, only. The eigenvalues are determined using the optimized Rayleigh-Ritz method and good engineering agreement is shown to exist with buckling parameters obtained by means of a finite element code.

Free vibrations of rectangular plates of exponentially varying thickness and with a free edge

Abstract Transverse vibrations of the structural system described in the title are analyzed by using classical plate theory and employing two different methodologies: the recently developed “optimized Kantorovich approach”; and a finite element algorithmic procedure. It is shown that the fundamental frequency coefficients obtained by using both techniques for a rather wide variation of the governing geometric parameters are in very good agreement. Lower frequency coefficients of the plate system determined by means of the finite element method are also presented.

Kirsch problem and the lower natural frequencies of a clamped square-plate

A clamped square-plate is subjected to a uniform state of stress in the x-direction. The present study deals with the basic question of determining the variation of the lower natural frequencies of transverse vibration of a plate as a small diameter, central hole is made in it, introducing a stress concentration field.