Unified approach for noisy nonlinear Mathieu-type systems

N. Sri Namachchivaya, Richard B. Sowers, H. J. Van Roessel

Research output: Contribution to conferencePaper

Abstract

The purpose of this work is to develop a unified approach to study the dynamics of a single degree of freedom system excited by both periodic and random perturbations. We consider the noisy Duffing-van der Pol-Mathieu equation as a prototypical single degree of freedom system and achieve a reduction by developing rigorous methods to replace, in some limiting regime, the original complicated system by a simpler, constructive, and rational approximation - a low-dimensional model of the dynamical system. To this end, we study the equations as a random perturbation of a two-dimensional weakly dissipative time-periodic Hamiltonian system. We achieve the model-reduction through stochastic averaging and the reduced Markov process takes its values on a graph with certain glueing conditions at the vertex of the graph. Examination of the reduced Markov process on the graph yields many important results, namely, mean exit times, probability density functions, and stochastic bifurcations.

Original languageEnglish (US)
Pages2447-2456
Number of pages10
StatePublished - Dec 1 2001
Event18th Biennial Conference on Mechanical Vibration and Noise - Pittsburgh, PA, United States
Duration: Sep 9 2001Sep 12 2001

Other

Other18th Biennial Conference on Mechanical Vibration and Noise
CountryUnited States
CityPittsburgh, PA
Period9/9/019/12/01

ASJC Scopus subject areas

  • Modeling and Simulation
  • Mechanical Engineering
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design

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    Sri Namachchivaya, N., Sowers, R. B., & Van Roessel, H. J. (2001). Unified approach for noisy nonlinear Mathieu-type systems. 2447-2456. Paper presented at 18th Biennial Conference on Mechanical Vibration and Noise, Pittsburgh, PA, United States.