Predictive lumped model for a tunable bistable piezoelectric energy harvester architecture

Abstract

In this article, we propose the modelling of a tunable Bistable Piezoelectric Energy Harvester (or BPEH) architecture. The former is a type of ambient energy converters that continue to gain attention due to their wideband frequency response. As the non-linear dynamics of BPEHs imply significant modeling complexity, dynamic lumped models are necessary to predict BPEHs’ dynamic response and should fit the type of architecture studied. The BPEH architecture of interest uses post-buckled beams to create bistability and an Amplified Piezoelectric Actuator (or APA) to convert the ambient vibrations. To date, no dynamic lumped models have been found in existing literature that account for both the electromechanical conversion and the dynamic behavior of buckled beams, with a specific focus on their axial and bending stiffness, for this BPEH architecture. Additionally, the proposed BPEH architecture offers buckling level tunability, which is achieved using an additional APA. Hence, the aim of this paper is to propose a new lumped model for a BPEH architecture which considers the effect of the post-buckled beams’ stiffnesses and of the additional APA through an elasticity factor κ ̅, called elasticity factor. This lumped model is established using Euler Lagrange equations and is experimentally validated on a tunable BPEH prototype. This validation shows an average relative error below 6% between the model’s predictions and experimental dynamic response of the prototype to an ascending frequency sweep, compared to an average relative error that’s below 15% for the model proposed in literature. Numerical simulations using the proposed model were made and lead to the conclusion that there is an optimal elasticity factor κ ̅ that ensures the maximum power output while maintaining the frequency bandwidth.