An Iterative Method for Large Modification of Vibration and Buckling Characteristics of Plates Simultaneously

Abstract

This article investigates a new iterative method based on the first and second order derivatives of eigenvalues which allows large modification of natural frequencies and buckling loads to be carried out simultaneously. A method is proposed for calculating the derivatives of eigenvalues and eigenvectors both in free vibration and buckling conditions. Using these eigen-derivatives, the first- and second-order Taylor expansions are presented for formulating the inverse approximate method or finding the necessary changes in design parameters for achieving simultaneous predefined shifts in natural frequencies and buckling loads. An iterative process is introduced for performing the modification in the case of considering large shifts in natural frequencies and buckling loads. By considering numerical case studies, it is shown that the proposed method can perform the predefined modification with an acceptable accuracy even for large perturbations in the objective functions.