Improving the performance of a two-sided vibro-impact energy harvester with asymmetric restitution coefficients

We study the influence of asymmetric restitution coefficients in a model of a two-sided vibro-impact energy harvester (VI-EH), considering the dynamical behavior and the implications for energy output. In the VI-EH, a ball moves freely within a forced cylinder and collides with a compliant dielectric polymer on either end, thus converting the motion into output voltage. We develop (semi-)analytical results for 1:1 periodic solutions, with alternating impacts on either end, focusing on the case of asymmetric restitution coefficients on the top and bottom of the cylinder. New types of 1:1 periodic solutions are found, with energy output clearly different from the symmetric setting. The analysis covers non-intuitive results, including the non-monotonic dependencies of the energy output on the asymmetric restitution coefficients. We find unexpected parameter ranges with improved levels of energy output, as well as stability results indicating that this output is robust to parameter fluctuations or external perturbations. Furthermore, by identifying parameter combinations that limit performance through asymmetries, we show how asymmetric restitution coefficients can counteract these detrimental effects. The analysis is based on maps for the dynamics between impacts, leading to a series of conditions for stable 1:1 periodic solutions in terms of the system parameters. We compare stability and bifurcation structure obtained analytically and numerically. The analysis shows possible regions of bi-stability between different behaviors that may not be captured by numerical approaches.