Large deflection effects in flexible energy harvesters

The effect of large deflection on the mechanical and electrical behaviors of flexible piezoelectric energy harvesters has not been well studied. A generalized nonlinear coupled finite element circuit simulation approach is presented in this article to study the performance of energy harvesters subjected to large deflections. The method presented is validated experimentally using three test examples consisting of (a) a static case, (b) a free vibration case, and (c) a forced vibration case. Under static conditions (when the transverse tip deflection exceeds a quarter of the cantilever length), large deflections cause geometric stiffening of the structure that reduces the tip deflection of the generator when compared to linear (i.e. small-deflection) behavior. For a cantilever generator under dynamic conditions, geometric stiffening, inertial softening, and nonlinear damping effects become significant. Large deflections both shift the resonant frequency and increase damping and can thus cause a significant reduction in output voltage when compared with small-deflection linear theory. In the finite element generator model studied in this article, these nonlinear dynamic effects become significant when the transverse tip deflection exceeds 35% of the beam length.