Discontinuity location on a Timoshenko beam by using a novel wave reflection technique

Based on the physical phenomenon that some propagating waves are partially reflected by discontinuities in waveguide structures, this paper proposes a novel discontinuity locating method which is potentially able to detect both the added and embedded discontinuities, such as supports and cracks. In this method, the reflection coefficients of a discontinuity can be obtained experimentally by using a generalized discontinuity approach without the information of the discontinuity position. On the other hand, these reflection coefficients can be derived from a reflection-coefficient prediction model in terms of the discontinuity position. By minimizing the error between the reflection coefficients from measurements and those from the prediction model, in the frequency bands in which the guided waves are sensitive to the discontinuity and can propagate with low decay rate, the discontinuity position parameter in the prediction model can then be identified. Two numerical cases of locating an added discontinuity and an embedded discontinuity on a beam are proposed to introduce the effectiveness of the method. Simulation results show that these two discontinuities can be located accurately with zero error. In practice, the accuracy of discontinuity locating may be influenced by some factors: (1) boundary conditions of the beam, (2) sizes and locations of the discontinuity, and (3) measurement noise. The investigation of these factors in simulation shows that this locating method is insensitive to the boundary conditions of the beam, effective to small size of the discontinuity, and robust to the measurement noise. Finally, three experiments were developed to locate an added discontinuity on a finite beam, a crack in an infinite beam with depth ratio of 1/2, and a crack in an infinite beam with depth ratio of 1/6, respectively. The corresponding locating errors of these three experiments are 0 percent, 0.077 percet and 0.154 percent.