Focusing of Lamb Waves in a Plate with Thickness Variation by the Inverse Filter

Abstract

In this study, a focusing method of Lamb waves is shown for a plate structure with thickness variation using the temporal-spatial inverse filter. An actuator is attached on the plate and a sensor is placed at the location which corresponds to the focusing location. Input and output signals of the actuator and sensor are analyzed in the frequency domain, and a Green function is obtained from the input-output relation. The inverse filter is constructed based on the Green function and the target focusing waveform. The waveform obtained by the inverse filter is used as the input waveform into the actuator to focus the Lamb wave at the initial sensor location. In this study, three-dimensional wave propagation analysis is performed by the elastodynamic finite integration technique (EFIT), and the focusing of the Lamb wave in the plate structure is simulated numerically. As a result, the emitted Lamb wave is focused at the initial sensor location and the target waveform is fairly reproduced by the target waveform. The wave focusing by a single actuator becomes possible by utilizing the effect of reflections at edges and steps of the plate. The temporal and spatial characteristics of the focused Lamb wave are shown and discussed.