Random Perturbations of Periodically Driven Nonlinear Oscillators

Nishanth Lingala, N. Sri Namachchivaya, Ilya Pavlyukevich, Walter Wedig

Research output: Contribution to journalConference article

Abstract

This paper develops a unified approach to study the dynamics of nonlinear oscillators excited by both periodic and random per- turbations. This study is motivated by problems that range from nonlinear energy harvesting to ship capsizing in random seas. The near resonant dynamics of such systems, in the presence of weak noise, is not well understood. Nonlinear systems driven by sufficiently strong periodic parametric excitation often display a range of phenomena from period doubling to chaos. In the presence of weak noise there are transitions between the domains of attraction of the stable periodic orbits. The effects of noisy perturbations on the passage of trajectories through the resonance zones is studied in depth using the large deviation theory.

Original languageEnglish (US)
Pages (from-to)91-100
Number of pages10
JournalProcedia IUTAM
Volume19
DOIs
StatePublished - Jan 1 2016
EventIUTAM Symposium Analytical Methods in Nonlinear Dynamics, 2015 - Frankfurt, Germany
Duration: Jun 6 2015Jun 9 2015

Keywords

  • averaged equations
  • exit times
  • large deviation
  • quasi potential
  • resonant dynamics

ASJC Scopus subject areas

  • Mechanical Engineering

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  • Cite this

    Lingala, N., Namachchivaya, N. S., Pavlyukevich, I., & Wedig, W. (2016). Random Perturbations of Periodically Driven Nonlinear Oscillators. Procedia IUTAM, 19, 91-100. https://doi.org/10.1016/j.piutam.2016.03.013