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A giant magnetostrictive material(GMM)model is developed based on the hysteretic nonlinear theory.The Gram-Schmidt regression method is introduced to determine the parameters of the model as well as the relationship between the material strain and the strength and frequency of magnetic field in the model.Through comparison,it is shown that this regression method has good performance in significance test.Then the model is applied to study the motion law of a circular plate in classical GMM transducer,which helps control the transducer rapidly and accurately.