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Dynamic modeling and resonant analysis of rotating internally connected laminated piezoelectric beams

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Abstract

In this paper, transient dynamic responses and frequency characteristics of a rotating internally connected laminated piezoelectric beam are analyzed and studied. Since the beam is compressed by the centrifugal force, frequencies decrease with the increase in the rotating speed (and centrifugal force), which can be called as the dynamic softening effect. When the frequency of increasing speed is gradually close to the decreasing the first frequency, the system resonance will occur. Nevertheless, the resonant rotating speed was rarely accurately calculated in the previous studies owing to ignoring the foreshortening effect that plays a significant role in the dynamic softening. To this end, a novel dynamic model of rotating internally connected laminated piezoelectric beams is developed. In this model, constitutive equations for metallic and piezoelectric material are considered, and the axial shortening displacement caused by the bending deformation is calculated for the foreshortening effect. The buckling rotating speeds obtained from the presented model show good agreement with those presented by the research considering the foreshortening effect, which well validates the model. Several examples are presented for investigating effects of radius, foreshortening effect, rotating speed on transient dynamic responses and frequency characteristics. The results show that beat and resonant vibrations can be orderly observed when the rotating speed is gradually close to the resonant speed. The resonant rotating speed is smaller than the buckling one. The simplified model ignoring the foreshortening effect leads to imprecise results including dynamic responses, buckling and resonant speeds.

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The datasets generated during and/or analyzed during the current study are available from the corresponding author upon reasonable request.

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Acknowledgements

The authors are grateful for Guangxi Natural Science Foundation Project (Project No. 2020GXNSFBA297010) National Natural Science Foundation of China (Project Nos. 12202110, 12232012, 12102191 and 11862001) and Innovation Project of Guangxi University of Science and Technology Graduate Education (Project No. GKYC202209).

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Authors and Affiliations

  1. School of Mechanical and Automotive Engineering, Guangxi University of Science and Technology, Liuzhou, 545006, China

    Jinjun Ma, Yuanzhao Chen & Wenjun Wu

  2. School of Sciences, Nanjing University of Science and Technology, Nanjing, 210094, China

    Liang Li & Dingguo Zhang

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  1. Jinjun Ma
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  2. Yuanzhao Chen
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  3. Wenjun Wu
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  4. Liang Li
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  5. Dingguo Zhang
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According to the authors’ contributions to this work, the author’s rank is JM, YC, WW, LL and DZ. YC is the corresponding author.

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Correspondence to Yuanzhao Chen.

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Ma, J., Chen, Y., Wu, W. et al. Dynamic modeling and resonant analysis of rotating internally connected laminated piezoelectric beams. Acta Mech 235, 355–368 (2024). https://doi.org/10.1007/s00707-023-03753-6

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  • DOI: https://doi.org/10.1007/s00707-023-03753-6

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