Quasi-periodic vibration-based energy harvesting is investigated in a delayed van der Pol–Duffing oscillator coupled to a delayed piezoelectric mechanism. It is assumed that the time delay in the mechanical subsystem is modulated around a mean value with a certain amplitude and frequency. The case of a delay-induced parametric resonance for which the frequency of the modulation is near twice the natural frequency of the oscillator is considered. The first- and second-step multiple scale methods are applied to obtain approximations of periodic and quasi-periodic solutions as well as the corresponding output powers. Bifurcation analysis is carried out to locate regions of existence of these solutions. The effect of different system parameters on the performance of quasi-periodic vibration-based energy harvesting is examined. The advantage of using quasi-periodic vibrations to extract energy over a broadband of system parameters away from the resonance is illustrated. Numerical simulations are conducted to validate the analytical predictions.

在与延迟压电机制耦合的延迟 van der Pol-Duffing 振荡器中研究了基于准周期性振动的能量收集。假设机械子系统中的时间延迟围绕具有特定幅度和频率的平均值进行调制。一的情况下，延迟引起的参数共振调制频率接近振荡器固有频率的两倍被考虑。应用第一步和第二步多尺度方法来获得周期和准周期解的近似值以及相应的输出功率。执行分岔分析以定位这些解的存在区域。检查了不同系统参数对基于准周期性振动的能量收集性能的影响。说明了使用准周期振动在远离共振的系统参数宽带上提取能量的优点。进行数值模拟以验证分析预测。