Exploring 1:3 internal resonance for broadband piezoelectric energy harvesting

Abstract

Recent literature has shown that the spectral characteristics of a harvester can be significantly improved by invoking internal resonance between the modes. Taking motivation from this premise, the present work analyzes the nonlinear dynamics and harvesting performance of a 1:3 internally resonant piezoelectric cantilever beam with a lumped mass under harmonic excitation. The governing modal equations are derived using Galerkin’s approach and Hamilton’s principle of least action. The method of multiple scales has been used to study the dynamics of the harvester in the proximity of primary resonances. The steady state periodic responses of the harvester are obtained using a pseudo-arc continuation technique and subsequently, their implications on the harvested power are discussed. The frequency responses of the harvested power are shown to boast significantly high magnitudes across a wide frequency band due to the energy transfer between the modes near the primary resonances. Results presented in the study show that the higher mode invoked through internal resonance plays a significant role in broadband power generation. The transfer of energy between the modes is found to occur only within a certain threshold of excitation level which in turn affects the magnitude of harvested power. Numerical simulations have also been carried out the results of which are compared against the analytical results. The outcomes of this first-hand analysis shall aid in the proposition of an efficient design for a broadband energy harvester.