Analysis of a One-Dimensional Waveguide Incorporating a Clearance-Type Nonlinear Energy Sink and Attached Energy Harvester

This work proposes a clearance-type electromechanical nonlinear energy sink (NES) to increase the electrical energy harvested from non-stationary mechanical waves, such as those encountered during impact and intermittent events. The key idea is to trap energy in the NES such that it can be harvested over a time period longer than that afforded by the passing disturbance itself. This leads to an asymmetrical, piece-wise nonlinear device whose functionality and analysis lie at the intersection of several current research topics, including wave-based energy harvesting, non-reciprocal wave propagation, nonlinear energy sinks (NES’s), and hybrid dynamical systems. The nonlinear energy sink concept explored uses a clearance-type nonlinearity, and resulting impact, to pass the energy of the propagating wave from a primary subdomain to a secondary subdomain where a significant portion of it is subsequently trapped and harvested. Moreover, unlike traditionally-studied single-DOF NESs, both subdomains of the NES (i.e., on either side of the clearance) contain displaceable degrees of freedom, significantly increasing the complexity of analytical solution approaches as compared to systems where one side is constrained by a known (or zero) displacement. Computational and analytical techniques are employed to optimize the energy sink and explore qualitative behavior (to include bifurcations). The analysis includes insight from Poincaré sections and bifurcation diagrams, with and without harvesters. Bifurcation diagrams and trends therein provide insight into the number and state of impact events at the NES as excitation amplitude increases. However, analytic formulations are found which quantify the relationship between the impact amplitude and the energy produced, parameterized by system properties such as the harvester effective resistance, the clearance gap, and the domain mass and stiffness. Importantly, a linear relationship between the input energy amplitude and the number of NES impacts has been observed and captured by an approximate, closed-form Poincaré map. In addition to this linear relationship, a closed-form Poincaré map is derived which maps one NES impact location to the next, greatly simplifying the analysis while providing an important tool for follow-on bifurcation studies. The results may justify further exploration in which complex structures (e.g., plates and/or three-dimensional structures) incorporate one or more of the clearance-type NESs to enhance non-stationary electroacoustic wave energy harvesting.