Surfing the High Energy Output Branch of Nonlinear Energy Harvesters

Hysteresis and multistability are fundamental phenomena of driven nonlinear oscillators, which, however, restrict many applications such as mechanical energy harvesting. We introduce an electrical control mechanism to switch from the low to the high energy output branch of a nonlinear energy harvester by exploiting the strong interplay between its electrical and mechanical degrees of freedom. This method improves the energy conversion efficiency over a wide bandwidth in a frequency-amplitude-varying environment using only a small energy budget. The underlying effect is independent of the device scale and the transduction method and is explained using a modified Duffing oscillator model.

Figure 1

Prototype and the proposed method. (a) The experimental prototype of the nonlinear EM harvester. (b) Proposed circuit to model the electrical actuation scheme. The mechanical to electrical energy conversion transducer consists of a spring-mass-damper system.

Figure 2

Transition from the LEB to the HEB. (a) Experimental result. The subplot indicates the load power as a function of the input frequency under different input accelerations without any electrical switching. The up sweep is indicated by the solid line and the down sweep by the dotted line. (b) Numerical result. The basin of attraction of the nonlinear oscillator is shown. High and low energy attractors are denoted by red and blue regions, respectively. Successful (yellow) and unsuccessful (green) switching are mapped in to the basin of attraction for varying the phase of the switching signal at fixed amplitudes (diamonds, 5 V; squares, 15 V; circles, 25 V).

Figure 3

Probabilistic study on the switching mechanism. (a) Mapping of successful (yellow) and unsuccessful (green) switching for varying the phase of the electrical switching signal with its amplitude. (b) Probability of successful switching as a function of the switching signal amplitude.

Figure 4

Electrical switching under frequency-amplitude-varying input vibration. Two input vibration trajectories ($R\to R^{\prime }$ and $S\to S^{\prime }$) are defined. Jump-up and -down frequencies are plotted in (a) and (b) as a function of input acceleration using auto-07p [35]. Output states: (a) without the electrical actuation and (b) with the electrical actuation. Numerical results show the improvement in load power due to electrical actuation for input trajectories (c) $R\to R^{\prime }$ and (d) $S\to S^{\prime }$.

Figure 5

The evolution of the net electrical energy under different acceleration levels. The negative slope from 20 to 20.2 s indicates that energy is supplied over that period of time.