Accession Number : AD0259493

Title :   RANDOM VIBRATION OF SYSTEMS WITH NONLINEAR RESTORING FORCES

Corporate Author : MASSACHUSETTS INST OF TECH CAMBRIDGE

Personal Author(s) : CRANDALL,STEPHEN H.

Report Date : 30 JUN 1961

Pagination or Media Count : 1

Abstract : Two procedures are discussed for studying the response of nonlinear systems to random excitation. The Fokker-Planck method is potentially applicable to a wide class of problems but the integrations required have only been effected in a few special cases. The equivalent linearization method is easy to carry out but is limited to small nonlinearities. It is demonstrated that to first order in the nonlinearity the equivalent linearization estimate of mean square stationary response is identical with that provided by the Fokker-Planck equation. A new equivalent linearization procedure for estimating the expected frequency of zero crossings in the random response is described and shown to give the same result as the Fokker-Planck equation. (Author)

Descriptors :   *STATISTICAL ANALYSIS, *VIBRATION, DAMPING, DIFFERENTIAL EQUATIONS, NUMERICAL INTEGRATION, NONLINEAR SYSTEMS, PARTIAL DIFFERENTIAL EQUATIONS

Distribution Statement : APPROVED FOR PUBLIC RELEASE