M. Mukhopadhyay

Vibration and stability analysis of stiffened plates by semi-analytic finite difference method, Part I: Consideration of bending displacements only

Abstract A semi-analytic finite difference method developed by the author for plates has been extended to the vibration and stability analysis of stiffened plates. The method, which is semi-analytic in nature, essentially consists of substituting the displacement function satisfying boundary conditions along two opposite edges into the free vibration and stability equations of the stiffened plate and then, by using suitable transformation, they are reduced to ordinary differential equations with constant coefficients. The effect of the stiffeners has been suitably incorporated. In this first part of a two-part paper, the bending displacements of the plate and the stiffener only are considered. Rectangular stiffened plates possessing different boundary conditions, mass and stiffness propertees and varying number of stiffeners have been analyzed. Comparison with published results indicates excellent agreement.

A semi-analytic solution for free vibration of annular sector plates

Abstract The paper describes a semi-analytical method in which the basic function in the circumferential direction satisfying the boundary conditions of the radial edges is substituted into the free vibration equation of the curved plate. By a suitable transformation, an ordinary differential equation is obtained. The resulting equation is solved by a finite difference technique. Tabulated results have been presented for annular sector plates possessing different boundary conditions. Excellent accuracy has been obtained wherever comparisons have been possible.

Vibration and stability analysis of stiffened plates by semi-analytic finite difference method, part II: Consideration of bending and axial displacements

Abstract A semi-analytic method developed by the author for plates is extended to the vibration analysis of eccentric stiffened plates. Eccentricity of the stiffeners gives rise to axial and bending displacement in the middle plane of the plate. This results in three coupled partial differential equations, which have been solved by the semi-analytic method. Rectangular stiffened plates having different boundary conditions and having varying mass and stiffness properties, as well as numbers of stiffeners, have been analyzed. Comparison with published results indicates good agreement.

Free vibration of rectangular plates with edges having different degrees of rotational restraint

Abstract A numerical method developed by the author has been used as a basis for determining natural frequencies of rectangular plates possessing different degrees of elastic restraints along the edges. The basic functions satisfying the boundary conditions along two opposite edges for such cases have been derived. Comparison of results with others that are available indicates excellent accuracy. Many new results have been presented.

A semi-analytic solution for free vibration of rectangular plates

Abstract By substituting the basic function satisfying boundary conditions along two opposite edges in one direction of the plate and then using a suitable transformation, the free vibration equation of the shape function of the plate is reduced to an ordinary differential equation. The resulting equation is expressed in finite difference form. The problem is thus transformed into an eigenvalue problem which on solution yields the natural frequencies of free vibration of plates. Examples have been presented for a variety of plates having different boundary conditions and having constant and variable thickness. Excellent accuracy has been obtained.

Free vibration of annular sector plates with edges possessing different degrees of rotational restraint

Abstract Results for the natural frequencies of annular sector plates possessing different degrees of elastic restraint along the edges are presented. The analysis is based on a numerical method developed by the author. The functions in the circumferential direction satisfying the boundary conditions along the radial edges, which are required in the analysis, are indicated. To the best of the authors knowledge, no previous results exist for such plates.

Vibration analysis of elastically restrained rectangular plates with concentrated mass

A numerical method developed earlier for determining natural frequencies of rectangular plates has been extended to include edges elastically restrained in translation and also to consider the effects of concentrated masses inside the plate. Many of the results are presented for the first time. Comparison of the results with those available showed good agreement.