Abstract
AbstractIn Part I of this paper, we have used spectral submanifold (SSM) theory to construct reduced-order models for harmonically excited mechanical systems with internal resonances. In that setting, extracting forced response curves formed by periodic orbits of the full system was reduced to locating the solution branches of equilibria of the corresponding reduced-order model. Here, we use bifurcations of the equilibria of the reduced-order model to predict bifurcations of the periodic response of the full system. Specifically, we identify Hopf bifurcations of equilibria and limit cycles in reduced models on SSMs to predict the existence of two-dimensional and three-dimensional quasi-periodic attractors and repellers in periodically forced mechanical systems of arbitrary dimension. We illustrate the accuracy and efficiency of these computations on finite-element models of beams and plates.
Funder
Swiss Federal Institute of Technology Zurich
Publisher
Springer Science and Business Media LLC
Subject
Electrical and Electronic Engineering,Applied Mathematics,Mechanical Engineering,Ocean Engineering,Aerospace Engineering,Control and Systems Engineering
Cited by
13 articles.
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