Energy harvesting in a nonlinear energy sink absorber using delayed resonators

This paper examines periodic and quasi-periodic (QP) vibration-based energy harvesting (EH) in a nonlinear energy sink (NES) absorber that is coupled to an electric circuit through a piezoelectric mechanism. For this investigation, we excite the primary system by harmonic force. To this system, we add linear delayed feedback controls implementations. The complexification-averaging (CX-A) method is employed to obtain approximate solutions. The analytically observed nonlinear behavior is numerically explained. In order to establish the feasibility of the control method, the energy balance of system is investigated. To systematically analyze the dynamic behaviors of the designed system, the stability of the system is studied using the reduced equations. We obtain the saddle-node (SN) and Hopf bifurcations by selecting specific parameters to establish the presence of periodic and QP solutions, after which we build and analyze the bifurcation diagrams. We exploit a time-delay mechanism implemented in a piezoelectric network and in a primary structure to enhance EH with good performance. Also, our findings demonstrate that the combination of time delay enables the system to harvest high periodic and QP powers. The QP power is obtained over a broad range of system parameters, yielding a reliable bandwidth of the harvester far from the hysteresis bandwidth.