Improvements in energy harvesting capabilities by using different shapes of piezoelectric bimorphs

The small amount of power needed by microelectronic devices opens up the possibility to convert part of the vibration energy present in the environment into electrical energy, using several methods. One such method is to use piezoelectric material as an additional layer in cantilever beams to harvest vibration energy for self-powered sensors. The geometry of a piezoelectric cantilever beam will greatly affect its vibration energy harvesting ability. Tapering and changing the configuration as ways to increase the generated output power of cantilever piezoelectric energy harvesters have gained popularity in recent years. In this work vibration energy harvesting via piezoelectric resonant bimorph cantilevers is studied and new designs for obtaining optimal piezoelectric energy harvesters are suggested. This paper deduces a very precise and simple analytical formula that can be used as a rule of thumb for calculating the resonant frequency of bimorph trapezoidal V-shaped cantilevers using the Rayleigh-Ritz method. This analytical formula is then analyzed using MATLAB as well as finite element methods and validated by ABAQUS simulation. Also, mathematical derivations for the output voltage of bimorph piezoelectric energy harvesters are presented and validated by simulation and experimental results. These formulas provide a new perspective that, among all the bimorph trapezoidal V-shaped cantilever beams with uniform thickness, the bimorph triangular tapered cantilever can lead to the highest resonant frequency and therefore maximum sensitivity, and by increasing the ratio of the trapezoidal bases the sensitivity decreases. Also, the output voltage and strain distribution show that the triangular cantilever has the highest efficiency and power density.