FRACTAL 2-LEVEL FINITE-ELEMENT METHOD FOR FREE-VIBRATION OF CRACKED BEAMS

The fractal two-level finite element method is extended to the free vi bration behavior of cracked beams for various end boundary conditions. A cracked beam is separated into its singlar and regular regions. Wit hin the singular region, infinite number of finite elements are virtur ally generated by fractal geometry to model the singular behavior of t he crack tip. The corresponding numerous degrees of freedom are reduce d to a small set of generalized displacements by fractal transformatio n technique. The solution time and computer storage can be remarkably reduced without sacrifying accuracy. The resonant frequencies and mode shapes computed compared well with the results from a commercial prog ram.