Fractal two‐level finite element method for free vibration of cracked beams

Article type: Research Article

Authors: Leung, A.Y.T.^; | Su, R.K.L.

Affiliations: School of Engineering, University of Manchester, Manchester M13 9PL, UK | Ove Arup & Partners, Hong Kong

Note: [] Corresponding author: Tel.: +44 161 275 4313; Fax: +44 161 275 4346; E‐mail: Andrew.Leung@ man.ac.uk.

Abstract: The fractal two‐level finite element method is extended to the free vibration behavior of cracked beams for various end boundary conditions. A cracked beam is separated into its singular and regular regions. Within the singular region, infinite number of finite elements are virturally generated by fractal geometry to model the singular behavior of the crack tip. The corresponding numerous degrees of freedom are reduced to a small set of generalized displacements by fractal transformation 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 program.

Journal: Shock and Vibration, vol. 5, no. 1, pp. 61-68, 1998