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Stochastic analysis of monostable vibration energy harvesters with fractional derivative damping under Gaussian white noise excitation

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Abstract

To the best of authors’ knowledge, the dynamical behaviors of vibration energy harvesters with fractional derivative damping have not been discussed by researchers with the help of the stochastic averaging method. As the fractional-order models are more accurate than the classical integer-order models, so it is necessary to investigate the dynamical behaviors of fractional vibration energy harvesters. This paper aims to investigate the stochastic response of monostable vibration energy harvesters with fractional derivative damping under Gaussian white noise excitation. First, we can get the equivalent stochastic system with the help of variable transformation. Then, the approximately analytical solutions of the equivalent stochastic system can be obtained by the stochastic averaging method. Third, the numerical results are considered as the benchmark to prove the effectiveness of the proposed method. The results indicate that the proposed method has a satisfactory level of accuracy. We also discuss the effect of system parameters on the mean square voltage.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Nos. 11472212, 11532011, 11702201). The first author (Y.-G. Yang) would like to thank the China Scholarship Council (CSC) for sponsoring his study in the USA.

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  1. Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, 710072, People’s Republic of China

    Yong-Ge Yang & Wei Xu

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  1. Yong-Ge Yang
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  2. Wei Xu
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Correspondence to Wei Xu.

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Yang, YG., Xu, W. Stochastic analysis of monostable vibration energy harvesters with fractional derivative damping under Gaussian white noise excitation. Nonlinear Dyn 94, 639–648 (2018). https://doi.org/10.1007/s11071-018-4382-z

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