ANALYSIS OF THE VARIATION OF FREQUENCIES FOR IMPERFECT RECTANGULAR-PLATES

The main purpose of the present work is to formulate a theory that can describe the influence of any initial geometric imperfection on the resonance frequencies of in-plane loaded rectangular plates of any boundary conditions and aspect ratio. The results indicate that the presence of imperfections of the order of a fraction of the plate thickness may significantly raise the resonance frequencies. Such an effect depends strongly on the type of boundary conditions, the mode shape of the imperfection and the mode shape of the vibration. Moreover, the results show interesting features concerning ''avoided crossing'' and ''coalescence'', a characteristic of eigenvalue problems when there is coupling between modes.