Galerkin scheme-based determination of survival probability of oscillators with fractional derivative elements

Antonina Pirrotta, Alberto Di Matteo, Jie Li, Yezeng Cheng, Pol D. Spanos

Risultato della ricerca: Articlepeer review

25 Citazioni (Scopus)

Abstract

In this paper, an approximate semi-analytical approach is developed for determining the first-passage probability of randomly excited linear and lightly nonlinear oscillatorsendowed with fractional derivative elements. The amplitude of the system response is modeled as one-dimensional Markovian process by employing a combination of the sto-chastic averaging and the statistical linearization techniques. This leads to a backward Kolmogorov equation which governs the evolution of the survival probability of the oscil-lator. Next, an approximate solution of this equation is sought by resorting to a Galerkin scheme. Specifically, a convenient set of confluent hypergeometric functions, related tothe corresponding linear oscillator with integer-order derivatives, is used as orthogonal basis for this scheme. Applications to the standard viscous linear and to nonlinear (Vander Pol and Duffing) oscillators are presented. Comparisons with pertinent Monte Carlo simulations demonstrate the reliability of the proposed approximate analytical solution
Lingua originaleEnglish
Numero di pagine9
RivistaJOURNAL OF APPLIED MECHANICS
Volume83
Stato di pubblicazionePublished - 2016

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

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