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Nonlinear magnetoelectric (ME) effect has drawn increasing interests due to its great potentials in nonlinear ME devices.In this paper,taking into account the quadratic magnetostrictive effect,a nonlinear ME coefficient was proposed to quantitatively characterize the harmonic distortion of ME frequency response.Moreover,we took a fresh look at the dynamic nonlinear ME response from the perspective of the shape evolution of hysteresis loops.As the frequency increases,the shape evolution of the ME hysteresis loop from crescent to butterfly and ellipse was observed.Taking into account the nonlinear magnetostrictive effect and the structural vibration,a dynamic hysteresis ME theory was established and validated by the experiment.It was found that the dynamic ME hysteresis was the combined result of competition between the first two orders of harmonic components and the corresponding phase shift.The former can be controlled by the frequency doubling and the mechanical resonance effect,and the latter is decided by the magnetostrictive loss and mechanical damping.These fundamental understandings of the ME harmonic hysteretic behaviors are benefit for the design and application of nonlinear ME devices.