@Article{cmes.2014.097.281,
AUTHOR = {H.T. Zhu},
TITLE = {A Solution Procedure for a Vibro-Impact Problem under Fully Correlated Gaussian White Noises},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {97},
YEAR = {2014},
NUMBER = {3},
PAGES = {281--298},
URL = {http://www.techscience.com/CMES/v97n3/27135},
ISSN = {1526-1506},
ABSTRACT = {This study is concerned with a solution procedure to obtain the probability density function (PDF) of a vibro-impact Duffing oscillator under fully correlated external and parametric Gaussian white noises. The proposed solution procedure consists of three steps. In the first step, the Zhuravlev non-smooth coordinate transformation is adopted to introduce an additional impulsive damping term, in which the original vibro-impact oscillator is converted into a new oscillator without any barrier. After that, the PDF of the new oscillator is obtained by solving the Fokker-Planck equation with the exponential-polynomial closure method. Last, the PDF of the original oscillator is formulated in terms of the methodology on seeking the PDF of a function of random variables. A numerical analysis on four different cases is conducted to examine the effectiveness of the proposed solution procedure. Comparison with the simulated result shows that the proposed solution procedure can provide a satisfactory PDF solution for the four cases. The tail region of the PDF solution is also approximated well. The numerical analysis also shows that the change of parametric excitation has a significant effect on the PDF distributions of displacement and velocity.},
DOI = {10.3970/cmes.2014.097.281}
}