Energy harvesting from transient free waves in a piezoelectric periodic chain: a settling-time approach

Conventional vibration energy harvesting is typically based on sustained external forcing and operation in the vicinity of a resonant frequency. This generally necessitates careful resonance tuning and can limit practical performance when the excitation is intermittent, transient, or not externally controlled. To address this limitation, we propose a framework for vibration energy harvesting through free wave propagation in a linear piezoelectric periodic chain formed by repeating an inverted cantilever beam with a tip mass and a piezoelectric patch attached near the base. No external forcing or excitation is applied to the system, and the harvesting potential is characterized in the regime of free wave propagation generated solely by initial conditions imposed on the tip mass. An analytical approach is developed to maximize the steady-state harvested power, and a closed-form relation is obtained between the optimal criterion for maximum steady-state power and the system design parameters. The concept of settling time is introduced and adapted to the free-wave response of unforced periodic systems, thereby providing a principled criterion for evaluating the maximum steady-state harvested power. This yields an independent framework for identifying the operating regime of the system parameters for optimal energy harvesting without the need for external forcing or resonance tuning. The proposed method thus represents a significant step beyond energy harvesting in forced single-degree-of-freedom oscillators near resonance, by exploiting the free-wave propagation characteristics of unforced periodic systems around an optimum frequency determined independently and solely by the system’s inherent structural, geometrical, and electrical parameters.