This paper investigates the nonlinear dynamic characteristics of a magnetically coupled piezoelectric energy harvesters under low frequency excitation, where the angle of external magnetic field is adjustable. The nonlinear dynamic equation with the identified nonlinear magnetic force is derived to describe the electromechanical interaction of variable inclination angle harvesters. The effect of excitation amplitude and frequency on dynamic behavior is proposed by using the phase trajectory and bifurcation diagram. The numerical analysis shows that a rotatable magnetically coupling energy harvesting system exhibits rich nonlinear characteristics with the change of external magnet inclination angle. The nonlinear route to and from large amplitude high energy motion can be clearly observed. It is demonstrated numerically and experimentally that lumped parameters equations with an identified polynomials for magnetic force could adequately describe the characteristics of nonlinear energy harvester. The rotating magnetically coupled energy harvester possesses the usable frequency bandwidth over a wide range of low frequency excitation by adjusting the angular orientation.

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