the lateral direction the beam is excited longitudinally, the governing equation of the system includes some nonlinear expression in the form of parametric excitation [8]. The most common mechanism of making the beam nonlinear is by placement of permanent magnets [9-17]. After modeling their systems and deriving the nonlinear governing equations most of these researchers have used numerical or experimental methods to solve the governing equations. Among the mentioned literature on magnetically nonlinear harvesters only Ref. [15] uses analytical perturbation methods, but they only solve the mechanical system and ignores the electromechanical coupling. An electromechanical model was introduced by the first and third author [18] to result the governing equations and predict vibration and power harvesting behavior of the proposed nonlinear hybrid energy harvesting device. Based on the model we designed and fabricate a prototype to show nonlinear vibrations characteristics for low frequency and low amplitude base oscillations. The current paper summarizes the results of experiments performed using the prototype. The paper follows by introducing the hybrid nonlinear harvesting device and driving the governing differential equations. Next we discuss the fabrication of the prototype and the test procedure. The experimental results are presented in three sections. The first two results sections are dedicated to mono-stable harvesting and the third section presents small vibrations, chaotic motion and limit cycle oscillations of the bi-stable harvester. The nonlinear hybrid energy harvesting device The hybrid nature of the nonlinear harvesting device proposed here is illustrated in Fig. 1. We use magnetic forces in our system to reduce nonlinear behavior. The magnetic force between the tip and base magnets is repulsive and therefore counteracts the elastic behavior. The existence of nonlinear forces acting on the beam introduces nonlinear hardening terms, which are explained in section 0. The piezoelectric element bounded to the beam harvests energy from beam deflection. As a novel approach we have placed electromagnetic coils in the system. When the beam vibrates the magnetic tip mass passes by the coils and generates electricity. The system is a hybrid energy harvester in the sense that, it uses two different methods (piezoelectric and electromagnetic transduction) for power harvesting. 462
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