Abstract—The effect of non-homogeneity on the free transverse vibration of thin rectangular plates of bilinearly varying thickness has been analyzed using generalized differential quadrature (GDQ) method. The non-homogeneity of the plate material is assumed to arise due to linear variations in Young’s modulus and density of the plate material with the in-plane coordinates x and y . Numerical re...

A thin flat rectangular plate supported on its edges and subjected to in-plane loading exhibits stable post-buckling behaviour. However, the introduction of a nonlinear (softening) elastic foundation may cause the response to become unstable. Here the post-buckling of such a structure is investigated and several important phenomena are identified, including the transition of patterns from strip...

in this paper, the free vibration response of a laminated composite rectangularplate supporting a rotating circular patch mass is studied. the two variable refined platetheory that employs only two unknown functions as against three in the case of simpleshear deformation theory is applied to define the third order displacement field of acomposite rectangular plate. the plate is considered to ha...

A semi-analytical approach to the elastic nonlinear stability analysis of rectangular plates is developed. Arbitrary boundary conditions and general out-of-plane and in-plane loads are considered. The geometrically nonlinear formulation for the elastic rectangular plate is derived using the thin plate theory with the nonlinear von Kármán strains and the variational multi-term extended Kantorovi...

In the traditional buckling analysis of rectangular plates the classical thin plate theory is generally applied, so neglecting the plating shear deformation. It seems quite clear that this method is not totally appropriate for the analysis of thick plates, so that in the following the two variable refined plate theory proposed by Shimpi (2006), that permits to take into account the transverse s...

An exact solution is obtained for three-dimensional deformations of a simply supported functionally graded rectangular plate subjected to mechanical and thermal loads on its top and/or bottom surfaces. Suitable temperature and displacement functions that identically satisfy boundary conditions at the edges are used to reduce the partial differential equations governing the thermomechanical defo...