The effects of edge cracks on the natural frequencies of cracked cantilever beams have been extensively studied by Wendtland (1972). These results are referred to by quite a number of related journal papers; the refernce is:
Wendtland D. A¨ nderung der biegeegenfrequenzen einer idealisierten Schaufel durch Risse. Ph.D. Dissertation, University of Karlsruhe; 1972.
Does anyone know how this can be accessed online, or atleast the complete set of results for eigenfrequency (first three modes of vibration) changes due to edge cracks at different positions and depths?
Check with Leibniz University of Hannover Library
Since this thesis is quite old, it might not be online at the University of Karlsruhe library. However, you could check with the library directly if they could send you a copy. If this doesnt work check with Leibniz University of Hannover library that will surely have a copy. If none of this works, then get in touch with some Indian student in Karlsruhe through social networking sites who could get the copy made and sent to you.
Best of Luck.
V. Hegadekatte, Consultant - Mathematical Modeling, Novelis Inc.