Electromechanical Modeling and Optimization of a Piezoelectric Energy Harvester Using Coupled Ordinary Differential Equations: A Computational Study

Wireless sensor networks and Internet of Things devices require autonomous power sources to replace traditional batteries. Piezoelectric energy harvesting presents a viable method by transforming surrounding mechanical vibrations into electrical power. However, basic uncoupled models frequently do not successfully forecast actual behavior. This paper presents a comprehensive computational study of a base-excited piezoelectric cantilever beam using a coupled electromechanical model. By combining the mechanical domain (Spring-Mass-Damper system) with the electrical domain through an electromechanical coupling coefficient, the simulation effectively models the two-way energy transfer. The system is numerically solved utilizing the SciPy library in Python. The research conducts three essential evaluations: transient time-domain response, load resistance optimization for impedance alignment, and frequency response examination. Findings reveal that optimal power is obtained when the electrical load aligns with the internal impedance of the piezo-element, yielding 70.89 μW at the resonant frequency of 63.6 Hz for the linear model. In contrast, the nonlinear bistable harvester demonstrated superior performance, achieving 4.0 mW at a low frequency of 0.8 Hz and a bandwidth broadening of 170%, validating the efficacy of the Snap-Through Buckling mechanism for low-frequency environments. The results offer a strong open-source structure for creating effective vibration energy harvesters.