One-dimension frequency-wavenumber-domain based model for ultrasonic waves generated by dual-array transducers

Array transducers can allow wavelength and frequency selectivity and can be used to generate different types of waves, such as ultrasonic bulk or guided waves. Dual-array transducers consist of two interlaced arrays, where the elements of each array are electrically connected. Therefore, by driving each array with a pair of phased pulses one can achieve a degree of wave generation control that allows unidirectional generation, unlike single array transducers that generate waves in both 0° and 180° directions with respect to the array's longitudinal axis. In this paper, we present a one-dimensional analytical model to determine the ultrasonic waves generated by dual-array transducers based on the excitability of the array in the frequency-wavenumber domain, the so-called operation region, determined by the joint spatial and temporal spectrum of the dual-array. We further exploited it to analyse the effectiveness of unidirectional generation with time-delayed excitation signals that provide ideal constructive or destructive interferences. The model also provides the time-domain received waveforms, which were compared to experimentally generated shear-horizontal ultrasonic guided waves, with a dual periodic permanent magnet array electromagnetic acoustic transducer, showing very good agreement. The adequate selection of the excitation signal allowed one to obtain up to about 40 dB unidirectionality experimentally.