Exact Vibration and Buckling Solution of Levy Type Initially Stressed Rectangular Thin Plates

This paper has focused on vibration and buckling of thin rectangular plates when at least two opposite sides are simply supported condition and subjected to axial and biaxial initial stresses. The relevant analysis is accomplished based on an exact solution method, free from any approximate method. First analytic techniques are used to discuss the free vibrations of plate. Then, natural frequencies and critical buckling loads are calculated. It is believed that through the present work, the exact closed-form characteristic equations and their associated eigenfunctions for the considered six cases are obtained for the first time.