Modeling of a broadband double-beam piezoelectric energy harvesting system

Resumo

In this work, a mathematical model, that describes the mechanical and electrical behaviors of an energy
harvesting system composed by a cantilever beam (primary beam) and a bimorph piezoelectric beam (energy
harvester) attached to the primary one, is presented. From a mechanical excitation (acceleration) at the base of the
primary beam, a voltage is generated in the piezoelectric. The primary beam is modeled as a multiple degrees of
freedom system, while the harvester is modeled as an equivalent spring (dynamic stiffness), which has the
mechanical and electrical characteristics of the piezoelectric beam. In order to obtain the equivalent stiffness, the
harvester is modeled as a single degree of freedom system. The equations of motion of the composite system are
obtained from Lagrange Equations. Using the generated voltage and the acceleration at the base of the primary
beam signals, a Frequency Response Function (FRF) was calculated, which can be used to identify a physical
system of this kind and to optimize its physical parameters in order to maximize power in a desired frequency
range. The numerical results showed the ability of the proposed compound system to generate energy over a wide
frequency range.