Response evolutionary power spectrum determination of chain-like MDOF non-linear structural systems via harmonic wavelets

A harmonic wavelets based technique is developed for determining the evolutionary power spectrum (EPS) matrix of the response of non-linear chain-like MDOF structural systems subject to a multi-component non-stationary stochastic excitation. Specifically, first a relationship between the evolutionar...

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Bibliographic Details
Published inInternational journal of non-linear mechanics Vol. 66; pp. 3 - 17
Main Authors Kong, Fan, Spanos, Pol D., Li, Jie, Kougioumtzoglou, Ioannis A.
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.11.2014
Subjects
Chains
Dynamical systems
Evolutionary
Evolutionary power spectrum
Harmonic wavelet
Harmonics
Hysteresis
Non-linear system
Nonlinear dynamics
Nonlinearity
Statistical linearization
Time-frequency analysis
Wavelet
Time-frequency analysis
Non-linear system
Statistical linearization
Evolutionary power spectrum
Hysteresis
Harmonic wavelet
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Summary:A harmonic wavelets based technique is developed for determining the evolutionary power spectrum (EPS) matrix of the response of non-linear chain-like MDOF structural systems subject to a multi-component non-stationary stochastic excitation. Specifically, first a relationship between the evolutionary power spectrum matrices of the excitation and of the system response is derived by using a recently proposed locally stationary wavelet based representation of non-stationary stochastic processes. The relationship can be construed as a direct extension of the celebrated spectral input–output relationship of the linear stationary random vibration theory. Further, a harmonic wavelets based statistical linearization technique is proposed for the case of MDOF non-linear systems with chain-like architecture systems and hysteretic non-linearities. Numerical examples include MDOF non-linear systems comprising the versatile Bouc–Wen hysteretic model. Pertinent Monte Carlo simulations demonstrate the reliability of the technique. •Evolutionary power spectrum (EPS) determination of stochastic dynamic systems.•EPS matrix relationship between non-stationary excitation and response.•Wavelet-based statistical linearization for non-linear/hysteretic MDOF structures.
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ISSN:0020-7462
1878-5638
DOI:10.1016/j.ijnonlinmec.2014.06.002