Distributed Parameter Modeling of Cantilevered-d₃₃-Mode Piezoelectric Energy Harvesters

Abstract

We present a distributed parameter model of a cantilevered-d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">33</sub> -mode piezoelectric harvester with interdigitated electrodes. The coupled mechanical and electrical circuit equations are derived, and the closed-form analytical solutions are obtained under Euler-Bernoulli beam assumptions and harmonic base translation with no rotatory motion. The steady-state voltage and vibratory response expressions, including all modes of vibrations, are reduced to single-mode expressions under modal excitation condition. The model is capable to predict the electrical response of the harvester for fundamental and higher modes of vibration. The computed results are verified with the experimental data for the fundamental mode available in the literature and found to agree well. The calculated single-mode voltage and power outputs are also in good agreement with the finite-element method simulation results using COMSOL.