Investigation Of The Nonlinear Model And Fractal Feature Of Magnetostrictive/Piezoelectric Laminated Transducer

Magnetostrictive/pizeoelectric laminated composites has been investigated for its giant magnetoelectric effect in room temperature.It is difficult to analyze the complex coupling between magnetic-mechanic-electric.The magnetoelectric transducer has strong nonlinear property.The linear model is limited in the given magnetic bias.The equivalent circuit method provides one popular model in linear and nonlinear theory.But it has some flaws in dealing with the equation of mechanical equilibrium.The usage of nolinear property should be explored.The fractal structure can take the advantage of nonlinear property.The nonlinear model is established based on the Jiles-Atherton model which is used to describe the magnetic hysteresis loops of magnetic materials.The main research points and conclusions are given in the follow list.(1)The nonlinear effect of magnetoelectric effect is dominated by the magnetostrictive phase of the laminated composites.The line constitutive equations and quadratic domain rotation model are discussed as discussing the principle of magnetostrictive material.The magnetoelectric effect is mainly affected by magnetic bias,the structure of transducer,work mode and resonant frequency.All this provides the base of our theoretical and experimental research.(2)The model of resonant magnetoelectric effect is deduced by using elastic method.This model is consist with the model given by equivalent circuit method which is used widely.But the result is in contradiction with the Gauss' s law in magnetic.To solve this problem,the second effect is introduced.That is to say,the additional induced magnetic field is considered when the exciting field is applied.The giving condition has some problem as simplifying the equation of mechanical equilibrium during modeling the resonant magnetoelectric effect.The system energy of the transducer is established by the linear constitutive equations and the equation of mechanical equilibrium.According the principal of minimum energy,the minimum value of the system energy is solved by using the Euler equations.The Lagrange multipliers are introduced to eliminate equality constraints.The results of solving show that the open circuit condition and constant magnetic flux should be chosen as simplifying the equation of mechanical equilibrium.These considerations lead to a more reasonable model of magnetoelectric effect.(3)The Jiles-Atherton model is chosen for describing the magnetic hysteresis loops of magnetostrictive materials.The PDE of nonhysteresis magnetization is concluded and solved by COMSOL which is very convenient for solve PDE and post processing.The piezomagnetic coefficient and permeability of magnetostrictive material are concluded by solving Jiles-Atherton model.The quadric domain rotation model is used during that process.The model of ?E effect is concluded by considering the magnetostrictive with vary magnetic bias.These give the nonlinear model of elastic compliance of magnetostrictive materials.(4)The loading effect of piezoelectric phase to magnetostrictive phase is considered by the equivalent parameters.The loading effect revised the parameters such as saturation magnetostriction,the effective coupling coefficients and the shape parameter of the anhysteresis magnetic field.These new parameters provide the strain model of the magnetoelectric transducer,and the nonlinear model of effective permeability,effective piezomagnetic coefficient and effective elastic compliance of magnetostrictive phase.These nonlinear models of magnetostrictive phase and the linear model of magnetoelectric effect lead to the nonlinear model of magnetoelectric effect.(5)The fractal magnetoelectric transducers are designed and fabricated with FeNi alloy and PVDF.The experiments of the fractal transducer shows that the 1st order Minkowski and 1st order Vicsek fractal transducer can lower the resonant frequency about 39% and 17%,respectively.The results demonstrate the fractal feature of the given transducer.The experiments also show the fractal transducer has the advantage of working in low magnetic bias because the stronger remanence which is originated from the fractal shape.The 1st order Minkowski fractal transducer is been optimized which shows the performance of fractal transducer can be further improved.