Fractional nonlinear energy sinks

doi:10.1007/s10483-023-2984-9

Applied Mathematics and Mechanics (English Edition) ›› 2023, Vol. 44 ›› Issue (5): 711-726.doi: https://doi.org/10.1007/s10483-023-2984-9

Fractional nonlinear energy sinks

Shengtao ZHANG¹, Jiaxi ZHOU¹, Hu DING², Kai WANG¹, Daolin XU¹

1. College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, China;
2. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy Engineering, School of Mechanics and Engineering Science, Shanghai University, Shanghai 200072, China

收稿日期:2023-01-03 修回日期:2023-02-28 发布日期:2023-04-24
通讯作者: Jiaxi ZHOU, E-mail: jxizhou@hnu.edu.cn
基金资助:
the National Natural Science Foundation of China (Nos.12122206, 11972152, and 12002122), the Natural Science Foundation of Hunan Province of China (No.2021JJ40092), and the Natural Science Foundation of Chongqing of China (No.cstc2021jcyj-msxmX0461)

Fractional nonlinear energy sinks

Shengtao ZHANG¹, Jiaxi ZHOU¹, Hu DING², Kai WANG¹, Daolin XU¹

1. College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, China;
2. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy Engineering, School of Mechanics and Engineering Science, Shanghai University, Shanghai 200072, China

Received:2023-01-03 Revised:2023-02-28 Published:2023-04-24
Contact: Jiaxi ZHOU, E-mail: jxizhou@hnu.edu.cn
Supported by:
the National Natural Science Foundation of China (Nos.12122206, 11972152, and 12002122), the Natural Science Foundation of Hunan Province of China (No.2021JJ40092), and the Natural Science Foundation of Chongqing of China (No.cstc2021jcyj-msxmX0461)

摘要/Abstract

摘要： The cubic or third-power (TP) nonlinear energy sink (NES) has been proven to be an effective method for vibration suppression, owing to the occurrence of targeted energy transfer (TET). However, TET is unable to be triggered by the low initial energy input, and thus the TP NES would get failed under low-amplitude vibration. To resolve this issue, a new type of NES with fractional nonlinearity, e.g., one-third-power (OTP) nonlinearity, is proposed. The dynamic behaviors of a linear oscillator (LO) with an OTP NES are investigated numerically, and then both the TET feature and the vibration attenuation performance are evaluated. Moreover, an analogy circuit is established, and the circuit simulations are carried out to verify the design concept of the OTP NES. It is found that the threshold for TET of the OTP NES is two orders of magnitude smaller than that of the TP NES. The parametric analysis shows that a heavier mass or a lower stiffness coefficient of the NES is beneficial to the occurrence of TET in the OTP NES system. Additionally, significant energy transfer is usually accompanied with efficient energy dissipation. Consequently, the OTP NES can realize TET under low initial input energy, which should be a promising approach for micro-vibration suppression.

关键词: fractional nonlinearity, nonlinear energy sink (NES), targeted energy transfer (TET), micro-vibration control

Abstract: The cubic or third-power (TP) nonlinear energy sink (NES) has been proven to be an effective method for vibration suppression, owing to the occurrence of targeted energy transfer (TET). However, TET is unable to be triggered by the low initial energy input, and thus the TP NES would get failed under low-amplitude vibration. To resolve this issue, a new type of NES with fractional nonlinearity, e.g., one-third-power (OTP) nonlinearity, is proposed. The dynamic behaviors of a linear oscillator (LO) with an OTP NES are investigated numerically, and then both the TET feature and the vibration attenuation performance are evaluated. Moreover, an analogy circuit is established, and the circuit simulations are carried out to verify the design concept of the OTP NES. It is found that the threshold for TET of the OTP NES is two orders of magnitude smaller than that of the TP NES. The parametric analysis shows that a heavier mass or a lower stiffness coefficient of the NES is beneficial to the occurrence of TET in the OTP NES system. Additionally, significant energy transfer is usually accompanied with efficient energy dissipation. Consequently, the OTP NES can realize TET under low initial input energy, which should be a promising approach for micro-vibration suppression.

Key words: fractional nonlinearity, nonlinear energy sink (NES), targeted energy transfer (TET), micro-vibration control

中图分类号:

34A34
74H45

Shengtao ZHANG, Jiaxi ZHOU, Hu DING, Kai WANG, Daolin XU. Fractional nonlinear energy sinks[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(5): 711-726.

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Fractional nonlinear energy sinks

Fractional nonlinear energy sinks

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