Nonlinear Normal Modes of a Curved Beam and Its Response to Random Loading

VanDamme, Christopher I.; Allen, Matthew S.

doi:10.1007/978-3-319-54404-5_12

Cited by 1 publication

(3 citation statements)

References 13 publications

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“…We quantify the accuracy of each reduced NNM using the periodicity metric ϵ , as defined in ref. [48], i.e. ϵ=∥boldxTbold−boldx0∥∥boldx0∥, where x 0 is the displacement vector of the FE model at t = 0, which is imposed as an initial condition based on the reduced NNM, and x T is the displacement vector of the FE model after one period.…”

Section: Application To a Finite Element Modelmentioning

confidence: 99%

“…We quantify the accuracy of each reduced NNM using the periodicity metric , as defined in ref. [48], i.e.…”

Section: Application To a Finite Element Modelmentioning

confidence: 99%

“…It should be noted that, in addition to enabling the internal resonance to be modelled, the two-DOF ROM also leads to more accurate response predictions on the primary backbone curve. We quantify the accuracy of each reduced NNM using the periodicity metric , as defined in [48], i.e.…”

Section: Application To a Finite Element Modelmentioning

confidence: 99%

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Detecting internal resonances during model reduction

Nicolaidou

Hill

Neild³

2021

Proc. R. Soc. A.

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Model order reduction of geometrically nonlinear dynamic structures is often achieved via a static condensation procedure, whereby high-frequency modes are assumed to be quasi-statically coupled to a small set of lower frequency modes, which form the reduction basis. This approach is mathematically justifiable for structures characterized by slow/fast dynamics, such as thin plates and slender beams, and has been shown to provide highly accurate results. Nevertheless, selecting the reduction basis without a priori knowledge of the full-order dynamics is a challenging task; retaining redundant modes will lead to computationally suboptimal reduced-order models (ROMs), while omitting dynamically significant modes will lead to inaccurate results, and important features such as internal resonances may not be captured. In this study, we demonstrate how the error associated with static condensation can be efficiently approximated during model reduction. This approximate error can then be used as the basis of a method for predicting when dynamic modal interactions will occur, which will guide the reduction basis selection process. Equivalently, this may serve as a tool for verifying the accuracy of ROMs without the need for full-order simulations. The proposed method is demonstrated using a simple oscillator and a finite element model of a clamped–clamped beam.

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