Identification of Nonlinear Normal Modes of Structures using the Empirical Mode Decomposition Method

摘要

The Empirical Mode Decomposition (EMD), which combines with the Hilbert transform (HT), has been used successfully to identify the dynamic characteristics of linear multi-degree-of-freedom structures. In this study, the EMD method is applied to the identification of nonlinear normal modes (NNMs) of nonlinear multi-degree-of-freedom (MDOF) structures. It is shown that the intrinsic mode functions (IMFs), which are obtained by applying the EMD method to the structural response, agree quite well with the nonlinear modal responses obtained from the invariant manifold approach. A two-degree-of-freedom building model with nonlinear stiffness is used for illustration. The EMD method is applied to decompose the measured response of the building model. The resulting IMFs are compared with the corresponding nonlinear modal responses, including their instantaneous frequencies and time-dependent amplitudes from the HT method. The comparison indicates that the resulting IMFs from the EMD method can reveal the nonlinear modal responses. It is seen that this EMD-based technique is fairly accurate to determine the nonlinear stiffness characteristics of the building model. The result suggests that the IMFs can be used to determine the physical dynamic properties of nonlinear structures.