An investigation into resonant frequency of trapezoidal V-shaped cantilever piezoelectric energy harvester

Power supply is a bottle-neck problem of wireless micro-sensors, especially where the replacement of batteries is impossible or inconvenient. Now piezoelectric material is being used as an additional layer in cantilever beams to harvest vibration energy for self-powered sensors. However, the geometry of a piezoelectric cantilever beam will greatly affects its vibration energy harvesting ability. This paper deduces a remarkably precise analytical formula for calculating the fundamental resonant frequency of trapezoidal V-shaped cantilevers using Rayleigh-Ritz method. This analytical formula, which is very convenient for mechanical energy harvester design based on Piezoelectric effect, is then analyzed using MATLAB as well as finite element methods and validated by ABAQUS simulation. This formula raises a new perspective that, among all the trapezoidal V-shaped cantilevers with uniform thickness, the simplest triangular tapered cantilever, can lead to maximum resonant frequency and highest sensitivity and by increasing the ratio of the trapezoidal bases, the sensitivity decreases.