Theoretical analysis and general characteristics for nonlinear vibration energy harvesters

Abstract

Abstract In this paper, we present a systematic theoretical and numerical study of the output performance of nonlinear energy harvesters. The general analytical expression of output power for systems with different combinations of nonlinear stiffness and nonlinear damping, as well as symmetrical and asymmetrical systems, have been derived based on harmonic balance method, observing compliance with numerical results. We theoretically prove that there is a limit power for all nonlinear systems which is determined exclusively by the vibrator mass, excitation acceleration, and mechanical damping. The results also indicate that for symmetrical stiffness systems, the asymmetrical damping components have no effect on the output performance. Additionally, we derived semi-analytical solutions of the matching loads and numerically investigated the influence of nonlinear coefficients on the output power with matched load. When the load matches device parameters and is much larger than the internal resistance, the equivalent time-average damping is equal to the mechanical damping. Although the matching load and output power vary with the nonlinear coefficients, the normalized power and matching resistance ratio follow a power function, named matching power line, which is independent of the structural parameters. With the improvement of the equivalent time-average short-circuit damping in the vibration range, the normalized power moves to the right end of the matching power line, and the output power approach to the limit power. These conclusions provide general characteristics of nonlinear energy harvesters, which can be used to guide the design and optimization of energy harvesters.