Resonant and antiresonant frequencies of multiple cracked bar

Abstract

The natural frequencies or related resonant frequencies have been widely used for crack detection in structures by the vibration-based technique. However, antiresonant frequencies, the zeros of frequency response function, are less involved to use for the problem because they have not been thoroughly studied. The present paper addresses analysis of antiresonant frequencies of multiple cracked bar in comparison with the resonant ones. First, exact characteristic equations for the resonant and antiresonant frequencies of bar with arbitrary number of cracks are conducted in a new form that is explicitly expressed in term of crack severities. Then, the conducted equations are employed for analysis of variation of resonant and antiresonant frequencies versus crack position and depth. Numerical results show that antiresonant frequencies are indeed useful indicators for crack detection in bar mutually with the resonant one

Crack identification in beam by antiresonant frequencies

“…The authors of Refs. [21,22] have studied resonant and antiresonant frequencies of multiple cracked bars and proposed a useful procedure for crack identification in bar based on both resonant and antiresonant frequency equations. The present study aims at expanding the obtained in [21,22] results for beam structures.…”

“…[21,22] have studied resonant and antiresonant frequencies of multiple cracked bars and proposed a useful procedure for crack identification in bar based on both resonant and antiresonant frequency equations. The present study aims at expanding the obtained in [21,22] results for beam structures. Namely, first explicit equations for antiresonant frequency are established for multiple cracked beams that allow one to examine antiresonant frequencies in dependence upon not only crack location and depth but also measuring and driving collocation.…”