Vibration of cracked Kirchhoff's plates

Abstract

This paper deals with the eigenvalue problems of cracked Kirchhoff's plates. Free vibration problems are solved for a plate with a centrally located internal crack. The fractal two-level finite element method (F2LFEM) which combines the efficiency of fractal transformation technique and the advantages of conventional finite element formulation is used to model the singular and regular region of the plates. The Discrete Kirchhoff's Triangular (DKT) elements with infinitesimal mesh are employed and the number of unknowns is reduced by interpolating the nodal displacements by means of global shape functions derived from the analytical solution. New element matrices need not be generated. Numerical results for natural frequencies are compared with the work of other investigators. Good agreement of results is observed.