Perturbation method applied to vibration monitoring of slotted beams

Abstract

Vibration signals can be used in monitoring the structural integrity of steel beams. If the beams are cracked or slotted, the resonant frequencies will decrease and the mode shapes will change depending on the size and the location of the defects. The current study involves applying a perturbation method in prediction of resonant frequencies and mode shapes of a slotted beam. Modal analysis techniques are used in estimation of modal parameters including resonant frequencies, damping, and mode shapes. The effect of using the modal analysis method on the frequency resolution will be discussed. A large discrepancy was observed between experimental frequency shifts and those predicted by the perturbation method for relatively large slots. As required by the method itself, perturbation to the system (in this case is slot) should be small, which will lead to small changes in modal parameters. These results are compared with those obtained previously [Man etal., J. Acoust. Soc. Am. 95, 2029–2037 (1994)] by solving the exact vibration equation for a slotted beam. It is clear that the perturbation technique is not accurate, although it does give correct qualitative predictions which are not readily apparent with the other approach.