Global nonlinear distributed-parameter model of parametrically excited piezoelectric energy harvesters |
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Authors: | A Abdelkefi A H Nayfeh M R Hajj |
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Institution: | 1. Virginia Tech, Blacksburg, VA, USA
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Abstract: | A global nonlinear distributed-parameter model for a piezoelectric energy harvester under parametric excitation is developed.
The harvester consists of a unimorph piezoelectric cantilever beam with a tip mass. The derived model accounts for geometric,
inertia, piezoelectric, and fluid drag nonlinearities. A reduced-order model is derived by using the Euler–Lagrange principle
and Gauss law and implementing a Galerkin discretization. The method of multiple scales is used to obtain analytical expressions
for the tip deflection, output voltage, and harvested power near the first principal parametric resonance. The effects of
the nonlinear piezoelectric coefficients, the quadratic damping, and the excitation amplitude on the output voltage and harvested
electrical power are quantified. The results show that a one-mode approximation in the Galerkin approach is not sufficient
to evaluate the performance of the harvester. Furthermore, the nonlinear piezoelectric coefficients have an important influence
on the harvester’s behavior in terms of softening or hardening. Depending on the excitation frequency, it is determined that,
for small values of the quadratic damping, there is an overhang associated with a subcritical pitchfork bifurcation. |
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