Numerical simulation and investigation of the spatial focusing of time reversal A0 Lamb wave mode using circular piezoelectric transducers collocated on a rectangular plate

Abstract

This paper numerically simulates and investigates the spatial focusing of time reversal A0 Lamb wave mode using a pair of circular piezoelectric (PZT) transducers collocated on a rectangular plate. The poling directionalities of the collocated PZTs enable the selective sensing and actuating of A0 Lamb wave mode during a time reversal process. First, the reciprocity of elasto-dynamics is demonstrated between two distinct displacement fields induced by a point loading and an actuating PZT. Then, a numerical analysis scheme based on a virtual sensor model and the Mindlin plate theory is implemented to reduce huge computing time for simulating the time reversal process. The validity of the implemented numerical scheme is verified through comparison to the conventional finite element analysis in both forward and backward propagation of A0 Lamb wave mode. The performance of the spatial focusing of time reversal A0 Lamb mode is investigated through a parameter study with respect to truncation time and driving frequency of an input source. Finally, the implication of the parameter study is discussed.