Method of stochastic normal forms

N. Sri Namachchivaya, Y. K. Lin

Research output: Contribution to journalArticlepeer-review


-The method of normal forms, originally developed for deterministic non-linear dynamical systems, is extended to include stochastic excitations, with the objective of obtaining an optimal reduction of dimensionality of the system while retaining its essential dynamic characteristics. Similar to the deterministic case, the crucial step in the normal-form computation is to find the so-called resonant terms which cannot be eliminated through a non-linear change of variables. Subsequent to the reduction of dimensionality, the associated stochastic normal form is obtained using a Markovian approximation. It is shown that the second order stochastic terms must be retained, in order to capture the stochastic contributions of the stable modes to the drift terms of the critical modes. Furthermore, for a specific class of non-linear systems, the results obtained from the stochastic normal form analysis are the same as those obtained from an extended stochastic averaging procedure. Thus, for this particular class, the two methods are equivalent.

Original languageEnglish (US)
Pages (from-to)931-943
Number of pages13
JournalInternational Journal of Non-Linear Mechanics
Issue number6
StatePublished - 1991

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics


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