Computational Stochastic Dynamics Based on Orthogonal Expansion of Random Excitations

  • X. Frank Xu
  • George Stefanou
Part of the Computational Methods in Applied Sciences book series (COMPUTMETHODS, volume 26)


A major challenge in stochastic dynamics is to model nonlinear systems subject to general non-Gaussian excitations which are prevalent in realistic engineering problems. In this work, an n-th order convolved orthogonal expansion (COE) method is proposed. For linear vibration systems, the statistics of the output can be directly obtained as the first-order COE about the underlying Gaussian process. The COE method is next verified by its application on a weakly nonlinear oscillator. In dealing with strongly nonlinear dynamics problems, a variational method is presented by formulating a convolution-type action and using the COE representation as trial functions.


Power Spectral Density Trial Function Polynomial Chaos Expansion Orthogonal Expansion White Noise Excitation 
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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of Civil, Environmental and Ocean EngineeringStevens Institute of TechnologyHobokenUSA
  2. 2.Institute of Structural Analysis & Antiseismic ResearchNational Technical University of AthensAthensGreece

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