Comparative modeling of low-frequency piezomagnetoelastic energy harvesters

In order to design efficient low-frequency piezomagnetoelastic energy harvesters, an effective analytical model which considers the effects of the electromechanical coupling and the nonlinear magnetic force is required. In this paper, the harvester consists of a partially covered piezoelectric cantilever beam with a fixed magnet mass at the top of the magnet tip mass. A nonlinear distributed-parameter model based on Euler-Bernoulli beam theory and Galerkin discretization is developed. The used mode shapes in the Galerkin discretization take into account the fact that the magnetic force and the piezoelectric sheet do not cover the whole beam. In addition, we develop an approximated distributed-parameter model that is based on the classical mode shapes of a fully covered piezoelectric cantilever beam in the Galerkin discretization. These distributed-parameter models are compared with a lumped-parameter model and experimental measurements. The results show that the derived distributed-parameter model accurately predicts the experimental measurements and particularly the accompanying softening behavior. On the contrary, it is demonstrated that the approximated distributed-parameter and lumped-parameter models give erroneous predictions of the resonance region, the level of the harvested power, and the softening behavior. In order to investigate the effects of the load resistance and the softening behavior on the performance of the harvester, a parametric study based on the analytically validated model is then performed. The results show that the presence and importance of the softening behavior depends on the electrical load resistance. It is also demonstrated that the presence of the softening behavior plays an important role in the short-and open-circuit configurations.