Bistable Piezoelectric Flutter Energy Harvesting with Uncertainty

Abstract

The analytical formulation of piezoelectric flutter energy harvesting using a bistable material, while considering uncertainties in the model is presented in this paper. Bistable laminates provide the advantage of large deflection due to the nonlinear snap-through characteristics when exposed to external loading, and can therefore provide a suitable base for piezoelectric material in energy harvesting applications. A piezoelectric material that is bounded on the surface of bistable laminates, subjected to external loading, generates large strains and hence relatively higher electrical output energy, in comparison with the case where piezoelectric material is bonded on a regular surface, with analogous loading conditions. Although information regarding the external loading, material characteristics of the bistable laminate and the piezoelectric material, boundary conditions, and overall electrical circuit efficiency can be defined for analytical purposes, the exact model of the system is not readily accessible. The unavoidable uncertainties in the material, loading, and efficiency of a complex system call for a probabilistic approach. Hence, this paper provides a formulation that considers uncertainty bounds in obtaining a realistic model. Optimal Uncertainty Quantification (OUQ) is used in this paper, which takes into account uncertainty measures with optimal bounds and incomplete information about the system, as a well-defined optimization problem according to maximum probabilities, subjected to the imposed constraints. The OUQ allows the inspection of the solution for a span of uncertain input parameters, as a reliable and realistic model.