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

International Journal of Non-Linear Mechanics
DOI: 10.1016/j.ijnonlinmec.2014.06.002
  • Statistical Linearization
  • Harmonic Wavelet
  • Non-Linear System
  • Hysteresis
  • Evolutionary Power Spectrum
  • Time-Frequency Analysis
  • Mathematics


Abstract 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.

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