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Numerical and experimental investigations of bistable beam snapping using distributed Laplace force

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Abstract

We report a study of an elastic buckled beam undergoing a contactless magnetic actuation of Laplace type. The beam model is based on the elastica beam theory including the beam extensibility. The Laplace force is produced by an electric current travelling along the beam placed in a magnetic induction. The magnitude of the electric current is the control parameter and by increasing the electric current the beam switches from one stable state to the other one for a given beam end-shortening. The main purpose of the study is to investigate the bistable response, more precisely, the diagram of the electric current as function of the midpoint vertical displacement of the beam according to the magnet location along the elastic beam. The model equations are established and they are numerically solved using an algorithm developed for nonlinear boundary value problem. A second part of the study is devoted to experimental validation of the model and comparisons with the results extracted from the numerical solutions to the model equations. Especially, the comparisons ascertain with good accuracy the approach of the proposed bista-ble beam model. In addition, the influence of the model parameters on the bistable response is clearly identified.

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Acknowledgements

The research work reported in the paper has been supported by the research project BISCELTECH funded by Fonds Unique Interministériel (FUI-APP21).

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  1. CNRS, Institut Jean le Rond d’Alembert, UMR 7190, Sorbonne Université, 75005, Paris, France

    A. Amor, A. Fernandes & J. Pouget

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  1. A. Amor
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  2. A. Fernandes
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  3. J. Pouget
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Correspondence to A. Fernandes.

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Amor, A., Fernandes, A. & Pouget, J. Numerical and experimental investigations of bistable beam snapping using distributed Laplace force. Meccanica 57, 109–119 (2022). https://doi.org/10.1007/s11012-021-01412-5

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