Response and stability of a random differential equation: Part I-moment equation method

H. Benaroya, M. Rehak

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


A linear stochastic differential equation of order N excited by an external random force and whose coefficients are white noise random processes is studied. The external force may be either white or colored noise random process. Given the statistical properties of the coefficients and of the force, equivalent statistics are obtained for the response. The present solution method is based on the derivation of the equation governing the response autocorrelation function. The simplifying assumption that the response is stationary when the coefficients and input force are stationary is introduced. Another simplification occurs with the assumption that the response is uncorrected from the random coefficients. Closed-form solutions for the response autocorrelation function and spectral density are derived in conjunction with a stability bound.

Original languageEnglish (US)
Pages (from-to)192-195
Number of pages4
JournalJournal of Applied Mechanics, Transactions ASME
Issue number1
StatePublished - Mar 1989
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


Dive into the research topics of 'Response and stability of a random differential equation: Part I-moment equation method'. Together they form a unique fingerprint.

Cite this