Impurity detection in a chain of spherical particles using time reversal and highly nonlinear solitary waves

摘要

We present a numerical study on the application of time reversal principles to highly nonlinear solitary waves (HNSWs) propagating along a one-dimensional granular crystal. HNSWs are compact non-dispersive waves that have been recently investigated in many fields of engineering including lensing, impact absorption, and nondestructive evaluation. Time reversal is instead a method to reconstruct a wave at the location where the wave was originated by reversing the same wave scattered at any other point. The overall principle applied in the present research is that a solitary pulse can be induced by a piezo-actuator inserted in the chain; the pulse travels forward and is captured by a second piezo-actuator, acting as a sensor; here, the signal is reversed in the time domain and then reapplied by the second piezo-actuator; the reversed signal travels backward through the chain, is sensed by the first piezo-actuator, and is collected as a reconstructed signal of the original one. In this study, we hypothesize and verify numerically that the original and reconstructed pulses are identical if the chain is uniform, whereas the reversibility is broken if an impurity is introduced. Γ