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2024 | OriginalPaper | Chapter

Nonlinear Normal Modes of Highly Flexible Beam Structures Modelled Under the \(SE(2)\) Lie Group Framework

Authors : Amir K. Bagheri, Valentin Sonneville, Ludovic Renson

Published in: Nonlinear Structures & Systems, Vol. 1

Publisher: Springer Nature Switzerland

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Abstract

We compute the periodic responses of geometrically nonlinear beam structures modelled using the Special Euclidean \(SE(2)\) Lie group formulation using shooting and pseudo-arclength continuation. Nonlinear normal modes (NNMs) are calculated for a cantilever beam and are compared to those obtained using a reference displacement-based finite element (FE) model with von Kàrmàn strains. Some specificities of the shooting algorithm which are unique to the underlying Lie group framework are discussed.

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previous chapter Analyzing Nonlinear Structures with Random Excitation Using Integral Quadratic Constraints
next chapter Extension and Experimental Verification of an Efficient Re-analysis Method for Modified Nonlinear Structures
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Metadata
Title
Nonlinear Normal Modes of Highly Flexible Beam Structures Modelled Under the Lie Group Framework
Authors
Amir K. Bagheri
Valentin Sonneville
Ludovic Renson
Copyright Year
2024
Book
Nonlinear Structures & Systems, Vol. 1

Print ISBN: 978-3-031-69408-0

Electronic ISBN: 978-3-031-69409-7

Copyright Year: 2024

DOI
https://doi.org/10.1007/978-3-031-69409-7_15