Higher-frequency wavenumber shift and frequency shift in a cracked, vibrating beam

Explicit wavenumber shift and frequency shift expressions are derived for the resonances of a cracked, transversely vibrating beam. These explicit expressions apply to beams with both shallow and deeper cracks. The explicit expressions are approximate, however, and are therefore generally inaccurate for the fundamental beam mode, and for a crack located in a boundary near field. The explicit expressions indicate that wavenumber shift and frequency shift are approximately proportional to the potential energy in the uncracked beam at the (future) crack location. Experimental results are presented for a freely vibrating, free-free beam with a midspan, single-edge slot. Data was collected for bending about both the strong axis and the weak axis. The experimental wavenumber shift curves generally agree well with the theoretical wavenumber shift curves.