This paper presents the modeling and analysis of a nonlinear wideband vibration energy harvester (VEH) with an asymmetric restoring force. It is commonly recognized that a VEH based on a nonlinear resonator having an odd-symmetric hardening (or softening) restoring force can show wideband frequency characteristics due to its bent resonance peak while keeping its maximum power performance. In practice, however, it often happens that the restoring force has some asymmetry, for instance, due to a bias force (e.g. gravity), or irregular asymmetry in the geometry. In this paper, a hardening resonator with a constant bias force is particularly focused on, and its approximate steady-state solution is studied based on a newly proposed averaging method combined with harmonic balancing. The validity of the approximate solutions are verified by comparing them with numerical solutions. As a result of the approximate and numerical analyses, it is shown that the frequency response displays a resonance peak climbing along an S-shaped backbone curve which is because of the softening effect due to the quadratic nonlinearity stemming from the asymmetry, followed by the hardening nature of the restoring force. Consequently, the frequency response yields the coexistence of multiple stable steady-state solutions on both sides of the resonance peak, and the highest-energy orbit exhibits a well-defined wideband behavior.

Date Published: 21 March 2019
PDF: 8 pages
Proc. SPIE 10967, Active and Passive Smart Structures and Integrated Systems XIII, 109670N (21 March 2019); doi: 10.1117/12.2515423

Published in SPIE Proceedings Vol. 10967:
Active and Passive Smart Structures and Integrated Systems XIII
Alper Erturk, Editor(s)