Piezoelectric unimorph and bimorph cantilever configurations: Design guidelines and strain assessment

Abstract

Multi-stable configurations of piezoelectric harvester are quite successful in achieving the two important goals, the broadband frequency response and large orbit oscillations exhibiting periodic, multi-periodic, and chaotic solutions. However, in the quest of achieving large amplitude broadband frequency response, assessment of induced strain levels considering the limits on the strain in piezoelectric material has received minimal attention. In this context, the investigation presents analytical formulation for the assessment of induced strain and voltage(s) in piezoelectric unimorph and bimorph cantilevers. The formulation quantifies not only the induced voltages in individual piezoelectric layers of a bimorph, but also the equivalent voltages in parallel and series connection modes, respectively. Also, while computing the induced voltage in the first piezoelectric layer, the contribution from the induced voltage of second piezoelectric layer to the acting bending moment is captured in the formulation. The formulations are validated through the experiments and results from the literature. Further, we have applied two practically useful normalization schemes, the - and -normalizations to the analytical expressions. Using the two normalization schemes, influences of variation of substrate and adhesive layer thicknesses, elastic moduli of layers, and substrate-to-composite length fraction are visualized and discussed. Based on the results, summarized guidelines for design and selection of geometric and material parameters are presented, which may also be applicable for other sensing and actuation applications. At last, practically suitable ranges and optimum values for the normalized design variables are proposed.