Optimal unidirectional generation of a dispersive wave mode with dual-array transducer

Abstract

Array transducers are commonly used to generate several types of waves, such as ultrasonic guided waves. They consist of a series of periodic wave source elements, and thus define a nominal or dominant wavelength of generated waves. A common approach to generating waves in a single direction is to use two identical wave sources, or two arrays of sources forming a dual-array transducer, that are separated by a quarter wavelength. Then, one source is activated a quarter of a time period after the other. In this way, constructive interference arises in one direction, whilst destructive interference arises in the opposite direction, making the total wave source unidirectional. This principle assumes that the frequency content of the generated wave is monochromatic. When there is some frequency bandwidth to the wave generated, such as with finite-length pulses, one cannot satisfy simultaneously constructive and destructive interference in opposite directions with dual-array transducers. For a non-dispersive wave mode, ideal destructive interference for pulsed waveform is obtained if one of the sources is inverted relative to the other, so that, in theory, complete cancellation can be achieved. Moreover, most guided wave modes are dispersive, meaning that, different frequencies propagate at different phase speeds. This limits the amount of wave cancellation in one direction and constructive interference in the other. Here, we describe the operation of the dual-array transducer in the frequency–wavenumber domain and use it to propose two new excitation methods, based on a frequency-dependent phase-shift strategy, that is designed through the dispersion relationship of the wave mode of interest. These provide ideal constructive or destructive interferences for dispersive waves, and achieve optimal unidirectional generation behaviour for dispersive wave modes. The new methods were experimentally assessed with shear horizontal ultrasonic waves, generated by a dual periodic permanent magnet electromagnet acoustic transducer. The optimal excitation signal yielded up to 30 dB unidirectionality, when generating the dispersive SH1 wave mode in an aluminium plate.