Identification and Construction of Reduced Order Models for Infinite-Dimensional Systems in Nonlinear Elastodynamics
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Reduced order models for the dynamics of an exact nonlinear elastic rod are derived by projecting its full order coupled equations of motion onto a set of Proper Orthogonal Modes. These optimal modes are identified by POD analysis of the finite element dynamics. Numerical study of the reduced models suggests that the subspace spanned by the POD modes represents an invariant subspace of the dynamics inside which a normal mode of vibration resides and whose shape is close to that of the dominant POD mode.
Key wordsInfinite dynamical systems proper orthogonal decomposition reduced order models nonlinear normal modes invariant manifolds
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