Semi-implicit integration algorithm for stochastic analysis of multi-degree-of-freedom structures

Yasuki Ohtori, Billie F. Spencer

Research output: Contribution to journalArticlepeer-review


This paper presents a semi-implicit integration algorithm for random vibration problems that is appropriate for analyzing large structures, nonlinear hysteretic systems, and structural control problems. This semi-implicit approach results in a recursive expression for the mean and covariance response. A state-space representation of the equations of motion is adopted for deriving the algorithm. The solution of the state-space equations is first obtained, after which the expected value of the resulting equations is taken so as to obtain the first two moments. A stability condition for the method is also derived. Three numerical examples, a linear oscillator, a Duffing oscillator, and a multi-degree-of-freedom system with hysteretic supplemental damping devices, are provided to illustrate the effectiveness of the proposed method. Results compare well with Monte Carlo simulation, indicating that the semi-implicit integration algorithm is accurate and stable.

Original languageEnglish (US)
Pages (from-to)635-643
Number of pages9
JournalJournal of Engineering Mechanics
Issue number6
StatePublished - Jun 1 2002
Externally publishedYes


  • Algorithms
  • Damping
  • Large structures
  • Stochastic processes
  • Vibration

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering


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