Application of HHT Techniques to Nonlinear Dynamic Analysis of Trusses
Date Issued
2009
Date
2009
Author(s)
Chen, Chun-Teh
Abstract
In the Fourier analysis, the fundamental assumption of linear and stationary process is required for the data. Applying the Fourier analysis to those data generated from nonlinear systems may cause misunderstanding of the physical phenomena hidden in the data. On the other hand, the Hilbert-Huang transform (HHT) is considered more suitable for analyzing nonlinear and non-stationary data. HHT includes two major parts: (1) empirical mode decomposition (EMD): a sifting process by which the data can be decomposed into a collection of intrinsic mode functions (IMF) that admit well-behaved Hilbert transforms; (2) Hilbert transform: a type of transform by which the instantaneous frequency and amplitude can be calculated for any instant. The energy distribution being plotted in a 3-D energy-frequency-time space is designated as the Hilbert spectrum. A two-member truss system with the effect of geometric nonlinearity considered is taken as the example in this study. The dynamic response of such a system is numerically analyzed by the finite element method along with the Newmark method, with the corresponding parameters in the Duffing equation given in each case. By comparing the results obtained from both the FFT and HHT analyses in frequency domain, the dynamic behavior of the nonlinear system is systematically studied, especially with respect to the variation in frequency caused by the geometric nonlinearity, period-doubling, chaos phenomenon, and so on.
Subjects
truss
nonlinear
dynamic
chaos
Hilbert Transform
FFT
HHT
Type
thesis
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