A model for an extensional mode resonator used as a frequency-adjustable vibration energy harvester

In an effort to identify techniques for harvesting energy from ambient vibrations, a prototype device that utilizes stretching piezoelectric film to support a proof mass, with an adjustable support that allows the resonant frequency of the device to be easily altered, has been developed. This extensional mode resonator (XMR) device is described by a model developed in this paper that predicts the power that is harvested as a function of the frequency and amplitude of the external vibration, the elastic and piezoelectric materials properties, and the device geometry. The model provides design guidelines for the effects of device geometry and applied tension through an adjustable support that suggest a strong dependence on mechanical damping and a weak dependence on frequency, as opposed to a bending cantilever device. The model predictions are compared to experimental measures from a prototype device for frequencies between 120 and 180 Hz, and at accelerations between 0.1 and 10 m/s2. Up to 9 mW is generated from a device with a mass of ∼82 g, and over the range of frequencies tested the power harvested at 4 m/s2 is between 3 and 4 mW.