Resonant frequency of bimorph triangular V-shaped piezoelectric cantilever energy harvester

The concept of “energy harvesting” is to design smart systems to capture the ambient energy and to convert it to usable electrical power for supplying small electronics devices and sensors. The goal is to develop autonomous and self-powered devices that do not need any replacement of traditional electrochemical batteries. Now piezoelectric cantilever structures are being used to harvest vibration energy for self-powered devices. 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 bimorph V-shaped cantilevers using Rayleigh 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 bimorph V-shaped cantilevers and in comparison with rectangular one, the simplest tapered cantilever beam can lead to maximum resonant frequency and highest sensitivity. The derived formula can be commonly used as a relatively precise rule of thumb in such systems.