Non-standard reduction of noisy structural systems: Shallow arches

Lalit Vedula, N Sri Namachchivaya

Research output: Contribution to journalArticle

Abstract

The dynamics of a shallow arch subjected to small random external and parametric excitation is invegistated in this work. We develop rigorous methods to replace, in some limiting regime, the original higher dimensional system of equations 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 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 such as mean exit time, stationary probability density function.

Original languageEnglish (US)
Pages (from-to)71-80
Number of pages10
JournalAmerican Society of Mechanical Engineers, Applied Mechanics Division, AMD
Volume241
StatePublished - Dec 1 2000

ASJC Scopus subject areas

  • Mechanical Engineering

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