Methods of nonlinear random vibration analysis

Manohar, C.S.

doi:10.1007/bf02823196

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2016

2022

Publication Types

Select...

Article5

Relationship

Self Cite0

Independent5

Authors

Journals

Cited by 6 publications

(1 citation statement)

References 175 publications

(174 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The solution obtained by the method of weighted residue is influenced by the weighting functions. More comments on these numerical methods were given in the review article [37] and a monograph [38].…”

Section: Introductionmentioning

confidence: 99%

The closed-form solution of the reduced Fokker–Planck–Kolmogorov equation for nonlinear systems

Chen

Sun

2016

Communications in Nonlinear Science and Numerical Simulation

View full text Add to dashboard Cite

In this paper, we propose a new method to obtain the closed-form solution of the reduced Fokker-Planck-Kolmogorov equation for single degree of freedom nonlinear systems under external and parametric Gaussian white noise excitations. The assumed stationary probability density function consists of an exponential polynomial with a logarithmic term to account for parametric excitations. The undetermined coefficients in the assumed solution are computed with the help of an iterative method of weighted residue. We have found that the iterative process generates a sequence of solutions that converge to the exact solutions if they exist. Three examples with known exact steady-state probability density functions are used to demonstrate the convergence of the proposed method.

show abstract

Section: Introductionmentioning

confidence: 99%