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The dynamic model of an energy harvesting system with a bistable cantilever beam
Abstract
In recent years, a nonlinear energy harvesting system using piezo cantilever beam with two magnets placed near the free end of the beam is of great research interest. The most common method for modeling this system is to discretize spatially the beam with only one ansatz function and to assume a cubic elastic force caused by the magnetic field. The magnets are positioned so that the system exists two stable equilibrium positions and an unstable one. This modeling method resulted in a Duffing equation with a negative linear elastic term and a positive cubic restoring term. Although this model can describe the above bistablity, its sufficiency of the assumptions has not been thoroughly verified. This paper presents the experimental results on the sufficiency of the Duffing equation describing a mechanical system consisting of elastic beams and magnets, without piezos for the purpose of simplification. Therefore, a model was developed to determine the cubic restoring force of the system. The theoretical results on the dynamic response of the Duffing model with the harmonic excitations were compared with the experiments. The results are generally in good agreement, but limitations of the model are still observed, as the solutions of the model shift to higher frequencies compared to the experiments.
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