RANDOM VIBRATION OF SYSTEMS WITH NONLINEAR RESTORING FORCES

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)

Document Details

Document Type
Technical Report
Publication Date
Jun 30, 1961
Accession Number
AD0259493

Entities

People

  • Stephen H. Crandall

Organizations

  • Massachusetts Institute of Technology

Tags

DTIC Thesaurus Topics

  • Crossings
  • Doppler Effect
  • Equations
  • Excitation
  • Fokker Planck Equations
  • Frequency
  • Frequency Shift
  • Nonlinear Systems
  • Random Vibration
  • Stationary
  • Vibration

Fields of Study

  • Mathematics

Readers

  • Control Systems Engineering.
  • Plasma Physics / Magnetohydrodynamics