Analytical predictions of periodic oscillations in a piezoelectric energy harvester under combined aeroelastic and harmonic excitation

This work studies a piezoelectric energy harvester subjected to both fluid flow and harmonic excitation. A lumped parameter model that incorporates fluid–structure interaction is presented to analyze the effects of both fluid flow and harmonic excitation on the proposed harvester. The method of implicit mapping is employed to calculate the periodic displacement, voltage, and velocity oscillations. Stabilities and bifurcations of periodic oscillations are determined based on the eigenvalues of the resultant matrix of mapping structures. The displacement and voltage nodes of the proposed energy harvester varying with excitation amplitude and frequency are investigated. The maximum eigenvalue magnitudes are illustrated. Utilizing the periodic nodes of the displacement and voltage, the harmonic amplitudes and phases are calculated using the fast Fourier transform. The harmonic amplitudes of both displacement and voltage varying with excitation frequency are depicted. For the stable periodic responses, the implicit maps and numerical simulations are presented to demonstrate the effectiveness of the energy harvesting system. The theoretical analysis presented in this study can be useful for the design and optimization of the proposed energy harvester.