Nonlinear characteristics of damaged reinforced concrete beam from Hilbert-Huang transform

This note studies the signatures of nonlinear characteristics in the vibration response of a reinforced concrete beam with cracks using Hilbert-Huang transform with reference to their possible use for detecting damage in reinforced concrete structures. The measured vibration signal from different cracked states of the beam are decomposed into intrinsic mode function (IMF) using empirical mode decomposition with the Hilbert-Huang spectrum computed for each of them. The time history of the instantaneous frequency of the beam, obtained from the IMF, is found correlating with the opening and closure of cracks. The effects of amplitude modulation and the Gibb’s phenomenon in the instantaneous frequency fluctuation have been separately quantified. The acceleration-frequency or the amplitude-frequency relationship in one cycle of vibration show distinctly the nonlinear vibration characteristics, and the damping ratio and instantaneous frequency change could be two good indicators of damage in the reinforced concrete beam under study.