Simultaneous modification of vibration and buckling characteristics of plates using the first and second order eigenderivatives

In this paper, the first and second order derivatives of eigenvalues are used for modifying the natural frequencies and buckling loads of structures, simultaneously. A method is proposed for calculating the derivatives of eigenvalues and eigenvectors both in free vibration and buckling conditions. Using the eigenderivatives, the first- and second-order Taylor expansions are presented for formulating both the direct approximate method, which may be defined as calculating the change of each natural frequency or buckling load by modifying an arbitrary parameter of the system, and inverse approximate method or finding the necessary changes in design parameters for achieving simultaneous predefined changes in natural frequencies and buckling loads.