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.

本文研究了非线性能量汇 (NES) 吸收器中基于周期性和准周期性 (QP) 振动的能量收集 (EH)，该吸收器通过压电机制耦合到电路。在本研究中，我们通过谐波力激发主系统。对于这个系统，我们添加了线性延迟反馈控制实现。采用复合平均（CX-A）方法来获得近似解。对分析观察到的非线性行为进行了数值解释。为了建立控制方法的可行性，对系统的能量平衡进行了研究。为了系统地分析设计系统的动态行为，使用简化方程研究系统的稳定性。我们通过选择特定参数来建立周期性和 QP 解的存在来获得鞍节点 (SN) 和 Hopf 分岔，然后我们构建和分析分岔图。我们利用在压电网络和初级结构中实现的延时机制来增强具有良好性能的 EH。此外，我们的研究结果表明，时间延迟的组合使系统能够收获高周期性和 QP 功率。QP 功率是在广泛的系统参数范围内获得的，从而产生远离滞后带宽的可靠带宽。我们的研究结果表明，时间延迟的组合使系统能够收获高周期性和 QP 功率。QP 功率是在广泛的系统参数范围内获得的，从而产生远离滞后带宽的可靠带宽。我们的研究结果表明，时间延迟的组合使系统能够收获高周期性和 QP 功率。QP 功率是在广泛的系统参数范围内获得的，从而产生远离滞后带宽的可靠带宽。