11 April 2006 Identification of modal responses of hysteretic structures using Hilbert-Huang method
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Abstract
Hilbert-Huang method is proposed to identify of modal responses of hysteretic multi-degree-of-freedom (MDOF) structures under free vibration. In this study, a response time history is first decomposed into intrinsic mode functions (IMFs) using the empirical mode decomposition (EMD) method. Then, the Hilbert transform is applied to each IMF to obtain the instantaneous amplitude and frequency. Modal analysis of nonlinear structures, which treats the nonlinearity at each time step as a pseudo force, is used to uncouple the equations of motion in order to obtain the modal responses. The Bouc-Wen model is used to simulate the hysteretic behavior of a two-degree-of-freedom shear-beam building model. The IMF components of the displacement responses are compared with the modal responses obtained from the modal analysis, in which three cases are considered for the pseudo force. In Cases 1 and 2, the pseudo force is the hysteretic force without and with its linear component, respectively. The pseudo force in Case 3 is taken in the form that the stiffness matrix becomes the same as that of the linear building model. It is shown that the IMF components, their instantaneous amplitudes and frequencies agree quite well with those of the modal responses obtained from Case 1 of the modal analysis.
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Chun-Wing Poon, Chun-Wing Poon, Chih-Chen Chang, Chih-Chen Chang, } "Identification of modal responses of hysteretic structures using Hilbert-Huang method", Proc. SPIE 6174, Smart Structures and Materials 2006: Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems, 61743C (11 April 2006); doi: 10.1117/12.658355; https://doi.org/10.1117/12.658355
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