A new method for free vibration and buckling analysis of rectangular orthotropic plates

A new method for free vibration and buckling analysis of rectangular allotropic plates is presented. The proposed method differs significantly from previously published methods in that it allows obtaining practically exact results for free vibration and buckling of orthotropic plates. By enhancing the method of superposition, the boundary value problem is essentially reduced to an infinite system of linear algebraic equations. Of particular significance of this research is that the existence of bounded solution of the infinite system after elimination of the unknowns has been captured in an elegant, but quantitative way to converge upon any natural frequency or critical buckling load of the orthotropic plate to any desired accuracy. The theory is applied to the particular case of orthotropic plates with clamped edges, but it can be extended to other boundary conditions. Buckling analysis is carried out as a degenerate case of free vibration at zero frequency. Comparisons of computed results from the present theory with those available in the literature are made wherever possible and some noteworthy conclusions are drawn. (C) 2014 Elsevier Ltd. All rights reserved.