Numerical solution of some three-state random vibration problems

S. F. Wojtkiewicz, L. A. Bergman, B. F. Spencer

Research output: Chapter in Book/Report/Conference proceedingChapter


This paper reports some of the recent efforts by the authors to examine the random vibration of mechanical systems of large dimension. A finite element solution method for the stationary three-dimensional Fokker-Planck equation, employing sparse storage and iterative solution strategies, is outlined and then applied to several representative systems. The first of these is a linear oscillator subjected to a first order linearly filtered Gaussian white noise process. This problem is used to verify and assess the accuracy of the method. After verification, two Duffing systems are analyzed, one exhibiting unimodal and the other bimodal response characteristics. Finally, some comparisons of the finite element results with those from Monte Carlo simulation are made for the two nonlinear systems.

Original languageEnglish (US)
Title of host publication15th Biennial Conference on Mechanical Vibration and Noise
Number of pages9
Edition3 Pt A/2
StatePublished - 1995
EventProceedings of the 1995 ASME Design Engineering Technical Conference - Boston, MA, USA
Duration: Sep 17 1995Sep 20 1995

Publication series

NameAmerican Society of Mechanical Engineers, Design Engineering Division (Publication) DE
Number3 Pt A/2


OtherProceedings of the 1995 ASME Design Engineering Technical Conference
CityBoston, MA, USA

ASJC Scopus subject areas

  • General Engineering


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