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

Abstract

Piezoelectric cantilevers are widely used in sensing and energy harvesting devices. For bothapplications, a higher induced voltage from a given mechanical excitation is desirable toincrease the sensitivity or energy conversion efficiency of the devices. In this study, weexamined the effect of the length ratio of the nonpiezoelectric layer to the piezoelectriclayer on the induced voltage of the piezoelectric unimorph cantilever due to aconcentrated force applied at the cantilever tip. The cantilever was made of leadzirconate titanate (PZT)–stainless steel (SS) unimorph. The length of the PZT layerwas fixed while that of the SS layer was varied. The induced voltage per unittip displacement was obtained by measuring the induced voltage in the PZTlayer and dividing it by the corresponding tip displacement of the cantilever andthe induced voltage per unit force was obtained by dividing the induced voltageper unit tip displacement by the effective spring constant of the cantilever. Theresults showed that the induced voltage per unit force increased with an increasingSS/PZT length ratio, indicating that under constant force conditions, the optimal inducedvoltage occurs when the SS layer is longer than the PZT layer. In contrast, theinduced voltage per unit tip displacement exhibited a maximum when theSS/PZT length ratio is unity, indicating that under constant tip displacement conditions, theoptimal 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 tocorrelate the induced voltage of the cantilever to the tip displacement and force. Theexperimental results were consistent with the prediction of the theoretical analysis.