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Probabilistic maps on bistable vibration energy harvesters

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A Correction to this article was published on 17 October 2023

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Abstract

This paper analyzes the impact of parametric uncertainties on the dynamics of bistable energy harvesters, focusing on obtaining statistical information about how each parameter’s variability affects the energy harvesting process. To model the parametric uncertainties, we use a probability distribution derived from the maximum entropy principle, while polynomial chaos is employed to propagate uncertainty. Conditional probabilities and probability maps are obtained to investigate the effect of uncertainty on harvesting energy. We consider different models of bistable energy harvesters that account for nonlinear piezoelectric coupling and asymmetries. Our findings suggest a higher probability of increasing harvested power in the intrawell motion regime as the excitation frequency increases. In contrast, increasing the excitation amplitude and piezoelectric coupling are more likely to increase power in the chaotic and interwell motion regimes, respectively. An illustrative example is presented to emphasize the importance of investigating the influence when all parameters vary simultaneously.

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Data Availability

Enquiries about data availability should be directed to the authors.

Code availability

The simulations presented in this paper were performed using the computational code STONEHENGE—Suite for Nonlinear Analysis of Energy Harvesting Systems [33], which is available for free on GitHub [30].

Change history

Notes

  1. Normalization here means zero mean and unit standard deviation.

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Acknowledgements

The authors gratefully acknowledge the insightful discussions on the results presented in this paper with Professors Grzegorz Litak (Lublin University of Technology) and Marcelo Savi (Federal University of Rio de Janeiro).

Funding

This research was financially supported by the Brazilian agencies Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) under Finance Code 001, Conselho Nacional de Desenvolvimento Científico e Tecnológico under the Grants 306526/2019-0 and 305476/2022-0, and the Carlos Chagas Filho Research Foundation of Rio de Janeiro State (FAPERJ) under Grants 210.167/2019, 211.037/2019, and 201.294/2021.

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Authors and Affiliations

  1. São Paulo State University, Ilha Solteira, SP, Brazil

    João Pedro Norenberg & Samuel da Silva

  2. Rio de Janeiro State University, Rio de Janeiro, RJ, Brazil

    Americo Cunha Jr.

  3. University of São Paulo, São Carlos, SP, Brazil

    Paulo Sergio Varoto

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  1. João Pedro Norenberg
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  2. Americo Cunha Jr.
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  3. Samuel da Silva
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  4. Paulo Sergio Varoto
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Correspondence to João Pedro Norenberg.

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Norenberg, J.P., Cunha, A., da Silva, S. et al. Probabilistic maps on bistable vibration energy harvesters. Nonlinear Dyn 111, 20821–20840 (2023). https://doi.org/10.1007/s11071-023-08864-2

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