Study of the Resonant Frequency of Unimorph Triangular V-shaped Piezoelectric Cantilever Energy Harvester

The main aim of the vibration energy harvesters is to locally power autonomous devices such as wireless sensors. Generally, power levels are low and the environmental benefit of the technology is to replace batteries rather than saving energy per se. Piezoelectric vibrational energy harvesters are usually inertial mass based devices, where a cantilever beam with a piezoelectric outer layer is excited into resonance by a mechanical vibration source at the root of the cantilever beam. However, the geometry of a piezoelectric cantilever beam will greatly affect its vibration energy harvesting ability. This paper deduces a remarkably precise analytical formula for calculating the fundamental resonant frequency of unimorph V-shaped cantilevers using Rayleigh-Ritz method. This analytical formula, which is convenient for mechanical energy harvester design based on piezoelectric effect, is then validated by ABAQUS simulation. This formula raises a new perspective that, among all the unimorph V-shaped cantilever beams and in comparison with rectangular one, the simplest tapered cantilever can lead to highest resonant frequency and maximum sensitivity.