In this study, model derivations are carried out of a dynamical system under base excitations with a piezoelectric energy harvesting absorber as the tuned-mass-damper. Additionally, amplitude stoppers are included to the absorber in order to create a broadband resonant response, increasing the window of operational use for energy harvesting and system’s control. This study is unique in the fact that the energy harvester is coupled to the source of its excitation. A nonlinear reduced-order model is developed using Euler–Lagrange principle and the Galerkin method to accurately estimate the energy harvesting absorber’s displacement, harvested power, and the oscillating response of the primary structure. The nonlinear interaction of the energy harvesting absorber and the amplitude stoppers are the focus of this study, where an in-depth investigation of bifurcation points of the primary structure and energy harvesting absorber responses is performed. Due to a transfer of energy between the primary structure and the absorber, it is shown that a soft stopper with stiffness has great control of the primary structure with 60% of the uncontrolled amplitude being reduced, as well as an increase of the harvested energy. Medium stoppers with small initial gaps size and hard stoppers do not control the primary structure and show a decrease in the energy harvesting capabilities due to the activation of the nonlinear contact-impact interactions. These stoppers also generate aperiodic regions due to the possible presence of grazing bifurcations.

在这项研究中，模型推导是在基本激励下以压电能量收集吸收器作为调谐质量阻尼器的动力系统进行的。此外，吸收器中包含振幅限幅器，以产生宽带谐振响应，增加能量收集和系统控制的操作使用窗口。这项研究的独特之处在于能量收集器与其激励源耦合。使用欧拉-拉格朗日原理和伽辽金方法开发了非线性降阶模型，以准确估计能量收集吸收器的位移、收集的功率和主结构的振荡响应。能量收集吸收器和振幅限幅器的非线性相互作用是本研究的重点，其中对主要结构的分叉点和能量收集吸收器响应进行了深入研究。由于主要结构和减振器之间的能量传递，表明具有刚度的软塞对初级结构有很好的控制，减少了 60% 的不受控制的振幅，并增加了收集的能量。具有小初始间隙尺寸的中型塞子和硬塞子不能控制主要结构，并且由于非线性接触-冲击相互作用的激活，能量收集能力降低。由于可能存在掠夺分叉，这些塞子还产生非周期性区域。