An approximate method for simultaneous modification of natural frequencies and buckling loads of thin rectangular isotropic plates

In this paper, the first and second order derivatives of natural frequencies and buckling loads with respect to an arbitrary geometrical or physical property of a plate structure are calculated. Based on these eigenderivatives, and by using first and second order Taylor expansions, an approximate method is presented for simultaneous modification of natural frequencies and buckling loads. In the proposed method, the structural modification is considered as an inverse eigenvalue problem and calculated eigenderivatives are used for transforming this inverse problem to solving a system of algebraic equations. By solving this set of equations, the necessary changes in design parameters are calculated, in order to achieve predefined simultaneous shifts in natural frequencies and buckling loads. A plate with two boundary conditions is considered as a case study. The plate is divided into eight regions and the plate thickness in each region is considered as a design parameter. By considering several case studies, the required modification in design variables is calculated for achieving a predefined change in natural frequencies, buckling loads or simultaneous change of both. In each case, the calculated changes in design variables are implemented on the initial structure, and the changes in eigenvalues are computed using FE method. It is shown that the results from presented method compare very well with those obtained from a direct optimization procedure. (C) 2008 Published by Elsevier Ltd