TRANSVERSE VIBRATION OF CIRCULAR AND ELLIPTIC PLATES WITH QUADRATICALLY VARYING THICKNESS

Approximate values of the frequencies of transverse vibrations of elliptic and circular plates with clamped edges have been computed, using the Rayleigh-Ritz method. The thickness is assumed to vary quadratically from the center to the boundary such that it is constant along an ellipse (or circle) concentric with the boundary. The procedure has been investigated by varying the aspect ratio and the two parameters controlling the thickness. Convergence of the results is ensured by taking a sufficiently large number of terms in the approximation to the displacement. Comparison has been made with results available in special cases.