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Nonlinear vibration analysis of a circular composite plate harvester via harmonic balance

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Abstract

A lumped parameter transverse vibration model of a composite plate harvester is analyzed via harmonic balance approaches. The harvester is mainly composed of a piezoelectric circular composite clamped by two steel rings and a proof mass on the plate. The lumped parameter model is a 1.5 degree-of-freedom strongly nonlinear system with a higher order polynomial stiffness. A harmonic balance approach is developed to analyze the system, and the resulting algebraic equations are numerically solved by adopting an arc-length continuation technique. An incremental harmonic balance approach is also developed for the lumped parameter model. The two approaches yield the same results. The amplitude-frequency responses produced by the harmonic balance approach are validated by the numerical integrations and the experimental data. The investigation reveals that there coexist hardening and softening characteristics in the amplitude-frequency response curves under sufficiently large excitations. The harvester with the coexistence of hardening and softening nonlinearities can outperform not only linear energy harvesters, but also typical hardening nonlinear energy harvesters.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grants 51575334 and 11802170), the State Key Program of National Natural Science Foundation of China (Grant 11232009), the Key Research Projects of Shanghai Science and Technology Commission (Grant 18010500100), and the Innovation Program of Shanghai Municipal Education Commission (Grant 2017-01-07-00-09-E00019).

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Authors and Affiliations

  1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai, 200072, China

    Tian-Chen Yuan & Li-Qun Chen

  2. School of Urban Railway Transportation, Shanghai University of Engineering Science, Shanghai, 201620, China

    Jian Yang

  3. Department of Mechanics, Shanghai University, Shanghai, 200444, China

    Li-Qun Chen

  4. Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai, 200072, China

    Li-Qun Chen

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  1. Tian-Chen Yuan
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Correspondence to Li-Qun Chen.

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Yuan, TC., Yang, J. & Chen, LQ. Nonlinear vibration analysis of a circular composite plate harvester via harmonic balance. Acta Mech. Sin. 35, 912–925 (2019). https://doi.org/10.1007/s10409-019-00863-0

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