Characteristic equation for antiresonant frequencies of multiple cracked bars and application for crack detection

The present paper addresses study and use of antiresonant frequencies for multi-crack detection in bar. First, there is an established new form of the exact characteristic equations for resonant and antiresonant frequencies in longitudinal vibration of bars with a finite number of cracks. Some asymptotic approximations of the equations are therefore derived and examined to evaluate their applicability in solving the forward problem of the multiple cracked bar. Then, the characteristic equations established in this study are used for analysis of change in antiresonant frequencies due to cracks. Finally, based on the characteristic equations and analysis, an efficient procedure is proposed to detect a number of cracks from given resonant and/or antiresonant frequencies. Numerical examples have been examined to illustrate and validate the proposed theory applied for detecting single crack in fixed-free end bar and double cracks in bar with free ends.