Nonlinear modal identification of a steel frame

The nonlinear modal identification of a four-storey steel frame is presented in this paper including both the experimental and the analytical aspects. The first two bending modes of the frame were experimentally isolated by a single-point mono-harmonic excitation. The subsequent free decay vibration was measured and used for identification purposes. An original filtering procedure was developed in order to overcome the drawbacks of the common band-pass filters and to enhance the accuracy of the signals. The nonparametric identification of the structure was carried out through an expeditious procedure based on the analysis of the evolution of the apparent frequency and equivalent viscous damping coefficient as a function of the apparent amplitude of the free decay cycles. The results of this identification reveal that the structure is weakly nonlinear in stiffness and strongly nonlinear in damping, while the mode shapes remain linear within the range of measurements. Asymptotic nonlinear laws defined in the modal space where proposed to model both the stiffness and the damping. This is another original contribution in this paper. The proposed nonlinear model was fitted to the experimental data in the time domain. Results were excellent with fitting errors three orders of magnitude lower than those of a pure linear model.