There has been very limited work on the application of time reversal to the propagation of audible frequency waves in mechanical structures. The present work concentrates on the application of time reversal to the focusing of audible range, flexural waves in an infinite beam, and to the detection of local heterogeneity in such a beam. Practical applications of time reversal of flexural waves in structures include vibration energy focusing, detection of vibratory or acoustic sources, and detection of defects in mechanical structures. An analytical model of flexural wave propagation in the beam as well as sensing and emission using piezoelectric transducers is presented. Time reversal experiments are conducted and compared to the model results in either a homogeneous beam or a beam with point mass heterogeneities. In the various situations tested, it is shown that time reversal effectively compensates the spreading in time of the impulse due to the dispersive propagation of flexural waves. One interesting aspect of this property is the generation of large amplitude impulsive responses in the beam using remote actuators. Finally, the "Decomposition de l'Operateur de Retournement Temporel" approach is examined to detect and localize point mass scatterers in the beam.

This paper presents an in situ damage identification method to characterize the thickness and location of a notch in a one-dimensional lap joint. The approach uses the propagation of flexural waves generated by a piezoceramic (PZT) to evaluate the global reflection coefficient of a complex structure such as a lap joint. A transmission line model (TLM) is used to describe the theoretical reflection coefficient from healthy and damaged lap joints. Parameters from the lap joint are identified in two steps from the experimental measurement of the reflection coefficient. The first step is a calibration step which gives, for the healthy lap joint, the length of the lap joint and distance between the measurement point and the lap joint. The identification of these parameters is performed by minimizing a cost function evaluated for different combinations of parameters. The second step allows us to obtain the parameters associated with the notch, which are its location and thickness. Several cases of healthy and damaged lap joints are conducted and very good results are achieved for the identification of the parameters.

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Time reversal of acoustic and structure-borne waves has been explored in recent years mostly for ultrasound and for nondispersive propagation, that is under frequency-independent wave velocity. In contrast, the case of time reversal in flexural beams presented here involves dispersive propagation, and is carried for frequencies below 5 kHz. The study has been started with analytical time reversal simulations in infinite homogeneous or heterogeneous beams (comprising point-mass scatterers). Experiments have also been realized on a 5 m beam with anechoic terminations and under transverse impact excitation. The time-reversal mirror was made of several thin piezoceramic elements bonded on the beam to sense the impulse response of the structure and re-emit its time-reversed image. The experimental results are in good agreement with the analytical results, and show that time spreading due to dispersive propagation of bending waves is successfully compensated by the time reversal operation. The presentation will illustrate the main results of the simulations and a comparison with the experiments.