Induced voltage of piezoelectric unimorph cantilevers of different nonpiezoelectric/piezoelectric length ratios

Piezoelectric cantilevers are widely used in sensing and energy harvesting devices. For both applications, a higher induced voltage from a given mechanical excitation is desirable to increase the sensitivity or energy conversion efficiency of the devices. In this study, we examined the effect of the length ratio of the nonpiezoelectric layer to the piezoelectric layer on the induced voltage of the piezoelectric unimorph cantilever due to a concentrated force applied at the cantilever tip. The cantilever was made of lead zirconate titanate (PZT)-stainless steel (SS) unimorph. The length of the PZT layer was fixed while that of the SS layer was varied. The induced voltage per unit tip displacement was obtained by measuring the induced voltage in the PZT layer and dividing it by the corresponding tip displacement of the cantilever and the induced voltage per unit force was obtained by dividing the induced voltage per unit tip displacement by the effective spring constant of the cantilever. The results showed that the induced voltage per unit force increased with an increasing SS/PZT length ratio, indicating that under constant force conditions, the optimal induced voltage occurs when the SS layer is longer than the PZT layer. In contrast, the induced voltage per unit tip displacement exhibited a maximum when the SS/PZT length ratio is unity, indicating that under constant tip displacement conditions, the optimal induced voltage occurs when the PZT layer and the SS layer have the same length. A theoretical analysis based on the Euler-Bernoulli beam theory was carried out to correlate the induced voltage of the cantilever to the tip displacement and force. The experimental results were consistent with the prediction of the theoretical analysis.