Eur. Phys. J. Plus (2021) 136: 278
https://doi.org/10.1140/epjp/s13360-021-01263-9

Regular Article

Enhancement of the performance of nonlinear vibration energy harvesters by exploiting secondary resonances in multi-frequency excitations

¹ Department of Mechanical Engineering, University of Manitoba, R3T 5V6, Winnipeg, Canada
² Institute of Water Resources and Hydropower Research, Northwest A&F University, 712100, Yangling, Shaanxi, People’s Republic of China
³ Key Laboratory of Agricultural Soil and Water Engineering in Arid and Semiarid Areas, Ministry of Education, Northwest A&F University, 712100, Yangling, Shaanxi, People’s Republic of China
⁴ Department of Mathematics, Huzhou University, 313000, Huzhou, People’s Republic of China
⁵ Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science & Technology, 410114, Changsha, People’s Republic of China
⁶ CONACyT-Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, 62490, Cuernavaca, Morelos, Mexico
⁷ Department of Mechanical Engineering, College of Engineering, Taif University, P.O.Box 11099, 21944, Taif, Saudi Arabia

^c chuyuming@zjhu.edu.cn
^d jose.ga@cenidet.tecnm.mx

Received: 14 January 2021
Accepted: 21 February 2021
Published online: 2 March 2021

Abstract

This study is concerned with utilizing secondary resonances in order to harvest energy from low-frequency excitations. Nonlinearities give rise to secondary resonances, which can potentially activate large-amplitude responses when the excitation frequency is a fraction of the fundamental frequency of the system. Such resonances offer an untapped and unique opportunity for harvesting vibratory energy from excitation sources with low-frequency components. This issue has propelled the current study. Based on multi-frequency excitation, we develop a novel theoretical framework for a piezomagnetoelastic energy harvester to enhance its performance. The proposed scheme is implemented in both monostable and bistable piezomagnetoelastic under low-frequency excitations. It is shown throughout the paper that when the excitation frequencies are certain fractions of the system's fundamental frequency, the combination and simultaneous resonance activate large-amplitude responses. Another advantage of the scheme is that the energy could be harvested from low-frequency ambient vibrations, which is a considerable concern in this field of study. Different responses of the system, such as low-amplitude and high-amplitude limit-cycle oscillations and chaotic motions, are studied through perturbation theory and numerical techniques. Various numerical tools, including phase portrait, Poincare section, and Lyapunov exponent, are used to explore complex dynamical behavior of the system. The performance of the harvester is also compared in different regions. Numeral simulations clearly confirm that the proposed framework dramatically enhances the performance of the energy harvester.