Details
| Originalsprache | Englisch |
|---|---|
| Titel des Sammelwerks | Nonlinear Structures and Systems |
| Untertitel | Proceedings of the 42nd IMAC, A Conference and Exposition on Structural Dynamics 2024 |
| Herausgeber/-innen | Matthew R. W. Brake, Ludovic Renson, Robert J. Kuether, Paolo Tiso |
| Herausgeber (Verlag) | Springer |
| Seiten | 95-98 |
| Seitenumfang | 4 |
| ISBN (elektronisch) | 978-3-031-69409-7 |
| ISBN (Print) | 9783031694080 |
| Publikationsstatus | Veröffentlicht - 8 Aug. 2024 |
| Veranstaltung | 42nd IMAC, A Conference and Exposition on Structural Dynamics, IMAC 2024 - Orlando, USA / Vereinigte Staaten Dauer: 29 Jan. 2024 → 1 Feb. 2024 |
Publikationsreihe
| Name | Conference Proceedings of the Society for Experimental Mechanics Series |
|---|---|
| ISSN (Print) | 2191-5644 |
| ISSN (elektronisch) | 2191-5652 |
Abstract
Vibrating slender structures often deform considerable, which trigger nonlinear behavior. For example, when the curvature is no longer small, the equations of motion contain nonlinear terms, which are often neglected assuming small vibration amplitudes. In this chapter, we experimentally observe nonlinear vibration behavior of a slender beam under harmonic excitation. We excite the bending modes of the beam and observe the forced response for different excitation levels. The frequency response shows a softening behavior with a jump phenomenon. The nonlinearity is more pronounced in higher bending modes but is already detected in the first clamped free bending motion. The experimental results are compared with an analytical approximation using the single nonlinear mode theory. The single-mode approach is appropriate for isolated modes and predicts a softening Duffing equation as a minimal nonlinear model of geometrically nonlinear beams. Finally, we obtain the governing equations directly from the measurements utilizing data-driven techniques. The underlying nonlinear differential equation is derived using test functions and sparse identification. The identified parameters are then compared to the analytical model.
ASJC Scopus Sachgebiete
- Ingenieurwesen (insg.)
- Allgemeiner Maschinenbau
- Ingenieurwesen (insg.)
- Numerische Mechanik
- Ingenieurwesen (insg.)
- Maschinenbau
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- BibTex
- RIS
Nonlinear Structures and Systems : Proceedings of the 42nd IMAC, A Conference and Exposition on Structural Dynamics 2024. Hrsg. / Matthew R. W. Brake; Ludovic Renson; Robert J. Kuether; Paolo Tiso. Springer, 2024. S. 95-98 (Conference Proceedings of the Society for Experimental Mechanics Series).
Publikation: Beitrag in Buch/Bericht/Sammelwerk/Konferenzband › Aufsatz in Konferenzband › Forschung › Peer-Review
}
TY - GEN
T1 - Modeling Nonlinear Beam Vibrations
T2 - 42nd IMAC, A Conference and Exposition on Structural Dynamics, IMAC 2024
AU - Tatzko, Sebastian
AU - Breunung, Thomas
AU - Wöhler, Hannes
AU - Förster, Alwin
AU - Kleyman, Gleb
PY - 2024/8/8
Y1 - 2024/8/8
N2 - Vibrating slender structures often deform considerable, which trigger nonlinear behavior. For example, when the curvature is no longer small, the equations of motion contain nonlinear terms, which are often neglected assuming small vibration amplitudes. In this chapter, we experimentally observe nonlinear vibration behavior of a slender beam under harmonic excitation. We excite the bending modes of the beam and observe the forced response for different excitation levels. The frequency response shows a softening behavior with a jump phenomenon. The nonlinearity is more pronounced in higher bending modes but is already detected in the first clamped free bending motion. The experimental results are compared with an analytical approximation using the single nonlinear mode theory. The single-mode approach is appropriate for isolated modes and predicts a softening Duffing equation as a minimal nonlinear model of geometrically nonlinear beams. Finally, we obtain the governing equations directly from the measurements utilizing data-driven techniques. The underlying nonlinear differential equation is derived using test functions and sparse identification. The identified parameters are then compared to the analytical model.
AB - Vibrating slender structures often deform considerable, which trigger nonlinear behavior. For example, when the curvature is no longer small, the equations of motion contain nonlinear terms, which are often neglected assuming small vibration amplitudes. In this chapter, we experimentally observe nonlinear vibration behavior of a slender beam under harmonic excitation. We excite the bending modes of the beam and observe the forced response for different excitation levels. The frequency response shows a softening behavior with a jump phenomenon. The nonlinearity is more pronounced in higher bending modes but is already detected in the first clamped free bending motion. The experimental results are compared with an analytical approximation using the single nonlinear mode theory. The single-mode approach is appropriate for isolated modes and predicts a softening Duffing equation as a minimal nonlinear model of geometrically nonlinear beams. Finally, we obtain the governing equations directly from the measurements utilizing data-driven techniques. The underlying nonlinear differential equation is derived using test functions and sparse identification. The identified parameters are then compared to the analytical model.
KW - Cantilever beam
KW - Data-driven modeling
KW - Duffing oscillator
KW - Geometric nonlinearity
KW - System identification
UR - http://www.scopus.com/inward/record.url?scp=85207834245&partnerID=8YFLogxK
U2 - 10.1007/978-3-031-69409-7_17
DO - 10.1007/978-3-031-69409-7_17
M3 - Conference contribution
AN - SCOPUS:85207834245
SN - 9783031694080
T3 - Conference Proceedings of the Society for Experimental Mechanics Series
SP - 95
EP - 98
BT - Nonlinear Structures and Systems
A2 - Brake, Matthew R. W.
A2 - Renson, Ludovic
A2 - Kuether, Robert J.
A2 - Tiso, Paolo
PB - Springer
Y2 - 29 January 2024 through 1 February 2024
ER -