Small and micro-scale energy harvesting is an essential and viable option for the powering of portable and maintenance free electronic devices, wireless sensor nodes, and similar applications. In this regard, piezoelectric harvesters have presented promising outcomes. This article provides a sequential, comprehensive, and informative survey of potential well based models and studies related to piezoelectric harvesters (PEH). Piezoelectric materials used for energy harvesting are discussed briefly, following which a non-dimensional generalized model is derived to set the discussion on a common platform. Dynamics of various potential well configurations are presented using the generalized model before discussing specific models and related studies. The survey is classified into symmetric and asymmetric potential well categories. Under the symmetric head, lumped and distributed parameter linear models and tuning methods for improving the broadband response are discussed. Subsequently, studies related to nonlinear mono-stable, bi-stable, and tri-stable potentials showing interwell, multi-periodic and chaotic oscillations with improved broadband response are discussed. The asymmetric section studies the influence of asymmetries on the performance of the mono-stable, bi-stable, and tri-stable configurations. Few other configurations outside the cantilever type PEH were mentioned, realizing the widespread research in this field. Important observations and future challenges for performance improvement are also discussed.

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Multi-stable configurations of piezoelectric harvesters 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 an analytical formulation for the assessment of induced strain and voltage(s) in piezoelectric unimorph and bimorph cantilevers. The formulation quantifies not only the induced voltage(s) 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 the 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 tp- and tt-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 are also applicable for other sensing and actuation applications. At last, practically suitable ranges and optimum values for the normalized design variables are proposed.