Impulse excitation of piezoelectric bimorphs for energy harvesting: a dimensionless model

Energy harvesting (EH) is a multidisciplinary research area, involving physics, materials science and engineering, with the objective of providing renewable sources of power sufficient to operate targeted low-power applications. Piezoelectric transducers are often used for inertial vibrational as well as direct excitation EH. However, due to the stiffness of the most common material (PZT), compact and light-weight harvesters have high resonant frequencies, making them inefficient at extracting low-frequency power from the environment. The technique of frequency up-conversion, in the form of either plucking or impulse excitation, aims to bridge this frequency gap. In this paper, the technique is modelled analytically with focus on impulse excitation via impact or shock. An analytical model is developed in a standard way starting from the Euler-Bernoulli beam equations adapted to a piezoelectric bimorph. A set of dimensionless variables and parameters is defined and a system of differential equations derived. Here the system is solved numerically for a wide range of the two group parameters present, covering piezoelectric coupling strength between PVDF and PMN-PT. One major result is that the strength of the coupling strongly affects the timescale of the process, but has only a minor effect on the total energy converted. The model can be readily adapted to different excitation profiles.