Equivalent Stochastic Quadratization for Single-Degree-of-Freedom Systems

Part of the Lecture Notes in Engineering book series (LNENG, volume 57)


The equivalent stochastic linearization method has proven to be a convenient and efficient analytical tool for computing the response statistics of nonlinear systems. This method was introduced by Krylov and Bogoliubov(1947) for nonlinear systems subject to deterministic excitation. It was first applied to nonlinear stationary systems with random excitations by Booton(1954) and later Caughey(1963). Later investigators generalized the method to multi-degree-of-freedom systems, nonstationary responses, and non-gaussian responses. Pertinent information can be found in Iwan and Yang(1972), Atalik and Utku(1976), Spanos(1980), Spanos(1981a), Beaman and Hedrick(1981). For a survey on linearization methods, see Spanos(1981b) and Roberts and Spanos(1989).


Displacement Response Impulse Response Function Volterra Series Resonance Response Hand Side Vector 
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Copyright information

© Springer-Verlag Berlin, Heidelberg 1990

Authors and Affiliations

  1. 1.Structural Dynamics Research CorporationMilfordUSA
  2. 2.Brown School of EngineeringRice UniversityHoustonUSA

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