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Vibration energy harvesting can solve the energy supplying problem of systems like wireless sensors networks.The Galfenol cantilever beam energy harvester is suitable for this application.According to the electromechanical conversion principle,the constitutive relation of Galfenol is built.A magnetization model is also established,based on the hysteresis model of Galfenol.Combining the magneto-mechanical coupling model,the constitutive relation of Galfenol and the electromagnetic induction law,the mathematical model of Galfenol vibration energy harvester is established.A hyperbolic curve-shaped cantilever beam is designed and its performance is compared to three types of cantilever beams: rectangle,trapezoidal,and triangle.The stress distribution,modal analysis and frequency response of these four shapes of beams are compared.The hyperbolic beam is more suitable for low frequency vibration harvesting.The strain on the beams,output voltage and power output response to these energy harvesters,under different natural vibration frequencies,are determined by simulation.Finally,the simulation results are compared to experimental electric outputs of all four types of prototype beams.The comparative study showed consistency between the experimental and the simulation results,and also that the peak-to-peak induction voltage value of the hyperbolic beam is larger than other shapes of energy harvesters,whose average value is at 269.8 mV.The maximum power output of the hyperbolic beam is 403.8 μW when connected with a 50 Ω resistance.