A multimodal electromagnetic vibration energy harvester based on a nonlinear quasi-periodic system is proposed. The multimodal approach and the nonlinearity are implemented in order to improve the output performances of the studied device. The present study investigates a periodic system composed of two weakly coupled magnets and mechanically guided by two elastic beams. The quasi-periodic system is obtained by varying the mass of one of the moving magnets which leads to the vibration energy localization in regions close to the imperfections introduced. This phenomenon is exploited to maximize the harvested energy. The mechanical nonlinearity is introduced by considering large displacements of the beams which is also investigated to maximize the harvested energy and to enlarge the bandwidth of the device. The quasi-periodic system is modeled by two coupled forced Duffing equations, which are solved using finite difference method combined with arc-length continuation method. The obtained results of the mass mistuning are analyzed and discussed in depth. It is shown that the introduction of the nonlinearity and the functionalization of the energy localization phenomenon lead to the enlargement of the bandwidth and the increase of the vibration amplitudes.

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