Phase symmetry analysis for nonlinear ultrasonic modulated signals

Nonlinear ultrasonic experiments typically require digital pass-band filters andadvanced signal processing tools to highlight low-amplitude nonlinear elasticeffects such as harmonics, subharmonics, and sidebands, which are used assignatures for the presence of damage. However, current signal processingtechniques cannot be used with dual periodic excitation without reducing sig-nal frequency resolution and severely altering measured waveforms. Thispaper reports the theoretical development of phase symmetry analysis fornonlinear ultrasound with dual periodic transmission. The proposed signalpostprocessing technique consists of determining the phase angles of transmit-ted waveforms that allow filtering modulated nonlinear ultrasonic waves fromthe measured signal spectrum. Experimental results validated theoretical pre-dictions and revealed that phase symmetry analysis method provides an easy-to-implement and reliable procedure to extract sidebands from the measuredsignal noise. Phase symmetry analysis with dual excitation has, therefore, thepotential to enable sensitive and efficient nonlinear ultrasound testing for vari-ous materials, damage scenarios, and applications