Abstract
The vibration of flexible rotating structures has been extensively investigated by the rotordynamics community. The analysis is usually performed via the finite element method using normal mode superposition. However, some interesting features of these structures may be hidden using a modal approach. In this paper, a wave-based approach is used to study the dynamic behavior of flexible rotating structures. Using a wave description, it is straightforward to show that the gyroscopic effect inherent to flexible rotating structures breaks the time-reversal symmetry. This corresponds to an asymmetric wave propagation, i.e., a forward-going wave and its corresponding backward-going pair travel with different wave speeds. In this paper, we show that this feature of flexible rotating structures makes them a natural mechanical circulator. On the other hand, we show that in the case of inhomogeneous flexible rotating structures designed as spectral gap elastic materials, i.e., phononic crystals or locally resonant metamaterials, the rotational speed has a strong influence in the location and width of the band gaps. The mathematical formulation of these problems have been presented by the authors elsewhere. Here, the conceptual aspects of these investigations are discussed under the light of original numerical simulation results.
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Acknowledgments
The authors are grateful to the Brazilian agencies, São Paulo Research Foundation (FAPESP - São Paulo, Brazil) and Coordination for the Improvement of Higher Education Personnel (CAPES - Brazil), for the financial support through project number 2014/19054-6 and to the Program Cátedras Franco-Brasileiras at State University of Campinas (UNICAMP). This research has also been performed within the framework of the 4TU.High-Tech Materials Research Programme “New Horizons in designer materials” (www.4tu.nl/htm).
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Beli, D., Brandão Silva, P., Mencik, JM., de França Arruda, J.R. (2019). Wave and Vibration Analysis of Rotating Periodic Structures by Wave-Based Methods. In: Cavalca, K., Weber, H. (eds) Proceedings of the 10th International Conference on Rotor Dynamics – IFToMM . IFToMM 2018. Mechanisms and Machine Science, vol 61. Springer, Cham. https://doi.org/10.1007/978-3-319-99268-6_36
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