On the non-linear behaviour of ultrasonic air-borne phased arrays. (26th May 2023) - Malkin, Robert; Kappus, Brian; Long, Benjamin; Price, Adam
Highlights: High amplitude air-borne acoustic arrays exhibit non-linear behaviour. The non-linearity is a function of both focal height and driving amplitude. Non-linear saturation can occur where the maximum possible acoustic pressure has been reached. Driving arrays at higher amplitudes shows a rapidly plateauing pressure produced. Acoustic saturation may be a suitable method of microphone calibration where the harmonics are outside of the measurement bandwidth. Abstract: Air-coupled phased arrays are an increasing area of academic and industrial interest. Their application to acoustic levitation and mid-air haptics relies on high amplitude focussed fields capable of generating very high acoustic pressures (e.g. >150 dB SPL). At these elevated pressures non-linear propagation effects can become significant, for example: the generation of harmonic frequencies, waveform asymmetry and acoustic saturation. In this work the basics of non-linear acoustics are presented with emphasis on energy loss mechanisms. Experimental work shows non-linearities as a function of focussing distance and driving amplitude. Large 2D microphone scans normal and tangential to the acoustic axis are carried out. Comparisons to linear models are made as well as modification to saturation equations developed for water-coupled fields. It is shown that saturation losses can become significant at elevated transducer amplitudes and focal distances. Metrics such as the waveform asymmetry, total harmonic distortion and energy loss are used to show the onset and magnitude of non-linearities. The volumetric experimental data shows how the fundamental and harmonic fields can differ in amplitude sufficiently such that harmonic amplitudes can exceed the fundamental. Suggestions are made on how to identify non-linearities and their general effect on air-coupled arrays and their applications.