6533b834fe1ef96bd129d662
RESEARCH PRODUCT
Stationary and non-stationary probability density function for non-linear oscillators
Giuseppe MuscolinoMarcello VastaGiuseppe Ricciardisubject
Stationary distributionCharacteristic function (probability theory)Applied MathematicsMechanical EngineeringMathematical analysisProbability density functionStationary sequencestochastic non-linear dynamics; Gram-Charlier expansions; approximate probability density functionGram-Charlier expansionsMechanics of Materialsstochastic non-linear dynamicsProbability distributionProbability-generating functionapproximate probability density functionSeries expansionRandom variableMathematicsdescription
A method for the evaluation of the stationary and non-stationary probability density function of non-linear oscillators subjected to random input is presented. The method requires the approximation of the probability density function of the response in terms of C-type Gram-Charlier series expansion. By applying the weighted residual method, the Fokker-Planck equation is reduced to a system of non-linear first order ordinary differential equations, where the unknowns are the coefficients of the series expansion. Furthermore, the relationships between the A-type and C-type Gram-Charlier series coefficient are derived.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1997-11-01 |