Electrical boundary conditions’ influence on a parabolically tapered piezoelectric energy harvester

Abstract

This research work presents the analytical modeling, simulation, and validation of a parabolically tapered piezoelectric energy harvester (PEH) subjected to different electrical boundary conditions. A fully coupled one-dimensional electromechanical model is formulated using Euler–Bernoulli beam theory, incorporating variable bending stiffness, mass distribution, and neutral-axis shift arising from the parabolic geometry. The model predicts frequency, voltage, and power response under base excitation and reveals the explicit influence of electrical loading on effective dynamic stiffness. Frequency-domain solutions are validated with ANSYS mechanical ANSYS parametric design language (APDL) simulations, showing less than 2% deviation. Results reveal that open-circuit conditions yield maximum voltage, while optimal power is obtained at a matched resistive load following the impedance matching principle. The parabolic tapering geometry enhances strain uniformity, lowers the resonant frequency, and improves energy conversion efficiency compared to rectangular designs. Parametric studies further demonstrate the impact of taper ratio, harvester length, and piezoelectric thickness on output characteristics. The proposed analytical framework provides a reliable and computationally efficient design tool for low-frequency vibration energy harvesters used in autonomous sensors and internet of things (IoT) applications.