Influence of asynchronous parametric excitation in stability maps of the simplest electromechanical system

Autores

  • Roberta Lima
  • Rubens Sampaio

DOI:

https://doi.org/10.5540/03.2023.010.01.0062

Palavras-chave:

Electromechanical systems, asynchronous parametric excitation, stability maps

Resumo

In this paper the influence of asynchronous parametric excitation in stability maps of the simplest electromechanical system is analyzed. The system is composed by two interacting subsystems, a mechanical and an electromagnetic, and it has the minimum number of elements necessary to be classified as an electromechanical system. The system does not have elements that can store potential energies, neither mechanical nor electromagnetic. The system dynamics is written in terms of 2 × 2 inertia matrix M and gyroscopic matrix G. Two parametric excitation terms are introduced in G. The terms have an amplitude ε, frequency Ω and asynchrony with respect to each other θ. For different values of θ, stability maps, in terms of ε and Ω, are constructed for the electromechanical system with the parametric excitation. In each map, it can be seen stability and instability regions of the trivial solution (system’s equilibrium) of the system. The objective of the paper is to analyze how the value of θ affects these stability and instability regions.

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Biografia do Autor

Roberta Lima

Pontifícia Universidade Católica do Rio de Janeiro

Rubens Sampaio

Pontifícia Universidade Católica do Rio de Janeiro

Referências

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A. Karev and P. Hagedorn. “Asynchronous parametric excitation: validation of theoretical results by electronic circuit simulation”. In: Nonlinear Dynamics 102 (2020), pp. 555–565. doi: 10.1007/s11071-020-05870-6.

R. Lima and R. Sampaio. “Modal analysis of an electromechanical system: a hybrid behavior”. In: Proceeding Series of the Brazilian Society of Computational and Applied Mathematics. Vol. 9. 1. 2022, pp. 1–7. doi: 10.5540/03.2022.009.01.0273.

R. Lima et al. “Comments on the paper ‘On nonlinear dynamics behavior of an electromechanical pendulum excited by a nonideal motor and a chaos control taking into account parametric errors’ published in this Journal”. In: Journal of the Brazilian Society of Mechanical Sciences and Engineering 41 (2019), p. 552. doi: 10.1007/s40430- 019-2032-0.

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W. Yang and S. Towfighian. “A parametric resonator with low threshold excitation for vibration energy harvesting”. In: Journal of Sound Vibration 446 (2019), pp. 129–143. doi: 10.1016/j.jsv.2019.01.038.

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Publicado

2023-12-18

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