NATURAL FREQUENCIES OF CIRCULAR AND ANNULAR PLATES WITH RADIAL OR CIRCUMFERENTIAL CRACKS

A Ritz solution is presented for the determination of the natural frequencies of free vibration of circular and annular plates with radial or circumferential cracks or slits through the full thickness. The approach uses a minimum number of sectorial plate elements which are joined together by means of artificial springs, the stiffness of which is permitted to become very high in order to satisfy the required continuity conditions. Numerical results are given for several plates for different crack positions and lengths. Through convergence studies and comparison with the few results available from the literature, the validity and accuracy of the solution is demonstrated.