Exploiting a nonlinear restoring force to improve the performance of flow energy harvesters

This paper investigates employing a nonlinear restoring force to improve the performance of flow energy harvesters (FEHs). To that end, a galloping FEH possessing a quartic potential energy function of the form $V=12μy2+14γy4$ is considered. This potential function is used to model either a softening (μ > 0, γ < 0), hardening (μ > 0, γ > 0), or bi-stable (μ < 0, γ > 0) restoring force. A physics-based model of the harvester is obtained assuming piezoelectric transduction and a quasi-steady flow field. The model is validated against experimental data and used to obtain a closed-form solution of the response by employing a multiple scaling perturbation analysis using the Jacobi elliptic functions. The attained solution is subsequently used to investigate the influence of the nonlinearity on the performance of the harvester and to illustrate how to optimize the restoring force in order to maximize the output power for given design conditions and airflow parameters. Specifically, it is shown that for similar design parameters and equal magnitudes of μ, and γ, a bi-stable energy harvester outperforms all other configurations as long as the inter-well motions are activated. On the other hand, if the motion of the bi-stable harvester is limited to a single well, then a harvester incorporating a softening nonlinear restoring force outperforms all other configurations. Furthermore, when comparing two FEHs incorporating the same type of restoring force at the optimal load and similar values of μ, then the FEH with the smaller γ is shown to provide higher output power levels.