Hilbert square demodulation and error mitigation of the measured nonlinear structural dynamic response

Abstract

The Hilbert square demodulation is a useful tool for the measured dynamic response analysis. However, if the Bedrosian theorem is violated for the measured response, it causes significant error in the demodulation process. Thus, to analyze the demodulation error in case of violated Bedrosian theorem, the analytic error quantification indexes are derived. The existed amplitude redistribution method and a novel recursive Hilbert transform method are further presented to mitigate the demodulation error. The efficiency is verified by an amplitude modulation signal and an amplitude modulation and frequency modulation signal with various sampling frequencies and noise levels. Moreover, a nonlinear Duffing system and a nonlinear cantilever beam structure are simulated as numerical examples. Finally, the dynamic response of a cantilever beam structure with a nonlinear bolted joint subjected to impact load is measured and analyzed. Both the numerical and experimental results show that the error mitigation technique is effective for the measured signal demodulation.