Eur. Phys. J. Plus (2018) 133: 510
https://doi.org/10.1140/epjp/i2018-12298-0

Regular Article

Theoretical analysis of vibration energy harvesters with nonlinear damping and nonlinear stiffness

¹ School of Mathematics and Statistics, Xidian University, 710071, Xi’an, Shaanxi, China
² School of Aeronautics, Northwestern Polytechnical University, 710072, Xi’an, China
³ Department of Automation, Lublin University of Technology, Nadbystrzycka 36, PL-20-618, Lublin, Poland
⁴ Department of Process Control, AGH University of Science and Technology, Mickiewicza 30, PL-30-059, Krakow, Poland

^* e-mail: zhoushengxi@nwpu.edu.cn

Received: 20 May 2018
Accepted: 30 September 2018
Published online: 11 December 2018

Abstract

Theoretical analysis of the vibration energy harvesters with nonlinear damping and nonlinear stiffness is provided to reveal their physical mechanism. Both the method of multiple scales and the method of averaging are employed to derive the theoretical solutions of the output voltage and power of the harvesters. The corresponding theoretical solutions are verified by direct numerical simulations. The nonlinear response characteristics are conducted by combining the stability analysis and the classification of the theoretical solutions. Especially, the dynamical hysteresis criterion which is used to determine the softening or hardening property is derived for enhancing energy harvesting performance. Meanwhile, the backbone curve is obtained. In addition, the influence of the excitation amplitude, the stiffness, the damping exponent, and the electromechanical coupling coefficient on the output power of the harvesters is explored. Overall, the physical mechanism of the harvesters is revealed and a framework for the optimization of maximizing the output power is provided.