Nonlinear energy harvesting with dual resonant zones based on rotating system

doi:10.1007/s10483-021-2698-8

Applied Mathematics and Mechanics (English Edition) ›› 2021, Vol. 42 ›› Issue (2): 275-290.doi: https://doi.org/10.1007/s10483-021-2698-8

Nonlinear energy harvesting with dual resonant zones based on rotating system

Dan WANG^1,2, Zhifeng HAO¹, Fangqi CHEN², Yushu CHEN³

1. School of Mathematical Sciences, University of Jinan, Jinan 250022, China;
2. College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China;
3. School of Astronautics, Harbin Institute of Technology, Harbin 150001, China

收稿日期:2020-07-26 修回日期:2020-10-08 发布日期:2021-01-30
通讯作者: Dan WANG E-mail:danwang2014518@hotmail.com
基金资助:
Project supported by the National Natural Science Foundation of China (Nos. 11702111, 11572205, and 11732014) and the Natural Science Foundation of Shandong Province of China (Nos. ZR2017QA005 and ZR2017BA031)

Nonlinear energy harvesting with dual resonant zones based on rotating system

Dan WANG^1,2, Zhifeng HAO¹, Fangqi CHEN², Yushu CHEN³

1. School of Mathematical Sciences, University of Jinan, Jinan 250022, China;
2. College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China;
3. School of Astronautics, Harbin Institute of Technology, Harbin 150001, China

Received:2020-07-26 Revised:2020-10-08 Published:2021-01-30
Contact: Dan WANG E-mail:danwang2014518@hotmail.com
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 11702111, 11572205, and 11732014) and the Natural Science Foundation of Shandong Province of China (Nos. ZR2017QA005 and ZR2017BA031)

摘要/Abstract

摘要： An electromagnetic nonlinear energy harvester (NEH) based on a rotating system is proposed, of which the host system rotates at a constant speed and vibrates harmonically in the vertical direction. This kind of device exhibits several resonant phenomena due to the combinations of the rotating and the vibration frequencies of the host system as well as the cubic nonlinearity of the NEH. The governing equation of motion for the NEH is derived, and the dynamic responses and output power are investigated with the multiple scale method under the 1:1 primary and 2:1 superharmonic resonant conditions. The effects of system parameters including the nondimensional external frequency, the rotating speed, and the nonlinear stiffness on the responses of free vibration for the system are studied. The results of the primary resonance show that the responses exhibit not only the resonant characteristics but also the nonlinear dynamic characteristics such as the saddle-node (SN) bifurcation. The coexistence of multiple solutions and the varying trends of responses are verified with the direct numerical simulation. Moreover, the effects of system parameters on the average output power are investigated. The results of the analyses on the two resonant conditions indicate that the large power can be harvested in two resonant frequency bands. The effect of resonance on the output power is dominant for the 2:1 superharmonic resonance. Moreover, the results also show that introducing the nonlinearity can increase the value of the output power in large frequency bands and induce the occurence of new frequency bands to harvest the large power. The efficiency of the harvested power could be improved by the combined effects of the resonance as well as the nonlinearity of the NEH device. Suitable parameter conditions could help optimize the power harvesting in design.

关键词: nonlinear energy harvester (NEH), resonance, output power, multiple scale method, rotating system

Abstract: An electromagnetic nonlinear energy harvester (NEH) based on a rotating system is proposed, of which the host system rotates at a constant speed and vibrates harmonically in the vertical direction. This kind of device exhibits several resonant phenomena due to the combinations of the rotating and the vibration frequencies of the host system as well as the cubic nonlinearity of the NEH. The governing equation of motion for the NEH is derived, and the dynamic responses and output power are investigated with the multiple scale method under the 1:1 primary and 2:1 superharmonic resonant conditions. The effects of system parameters including the nondimensional external frequency, the rotating speed, and the nonlinear stiffness on the responses of free vibration for the system are studied. The results of the primary resonance show that the responses exhibit not only the resonant characteristics but also the nonlinear dynamic characteristics such as the saddle-node (SN) bifurcation. The coexistence of multiple solutions and the varying trends of responses are verified with the direct numerical simulation. Moreover, the effects of system parameters on the average output power are investigated. The results of the analyses on the two resonant conditions indicate that the large power can be harvested in two resonant frequency bands. The effect of resonance on the output power is dominant for the 2:1 superharmonic resonance. Moreover, the results also show that introducing the nonlinearity can increase the value of the output power in large frequency bands and induce the occurence of new frequency bands to harvest the large power. The efficiency of the harvested power could be improved by the combined effects of the resonance as well as the nonlinearity of the NEH device. Suitable parameter conditions could help optimize the power harvesting in design.

Key words: nonlinear energy harvester (NEH), resonance, output power, multiple scale method, rotating system

中图分类号:

70K30
70K50

Dan WANG, Zhifeng HAO, Fangqi CHEN, Yushu CHEN. Nonlinear energy harvesting with dual resonant zones based on rotating system[J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(2): 275-290.

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Nonlinear energy harvesting with dual resonant zones based on rotating system

Nonlinear energy harvesting with dual resonant zones based on rotating system

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