Nonlinear Model And Vibrationreduction Performance Ofmagnetostrictive Periodicstructure With Shunt Circuit

Compared with the traditional periodic structure,the magnetostrictive periodic structure with shunt circuit can adjust its Bragg band gap and local resonance band gap by adjusting the bias magnetic field,stress and shunt elements to reduce vibration transmission which has good application prospects.However,the magneto-mechanical-electrical coupling nonlinearity of device is exhibited,which makes it difficult to design and estimate the performance of the device.The Young's modulus expression of the magnetostrictive material with shunt circuit is derived firstly.The performance of Young's modulus with shunt circuit is analyzed and a nonlinear dynamic model of the magnetostrictive rod periodic structure with shunt circuit is established.The material nonlinearity,device band gap and vibration reduction performance are analyzed.Finally,the electromechanical two-way coupled dynamic model of the magnetostrictive layered periodic structure and its vibration reduction performance are studied.The main work about this research is as follows:(1)Based on the magnetostrictive linear constitutive equation,Faraday's law and circuit theory,the Young's modulus expression of the magnetostrictive material with shunt circuit is derived.The influence law of the shunt element parameters on the Young's modulus with different shunt circuit is summarized and the calculation results and the experimental results are compared,which shows the correctness of the Young's modulus expression.(2)The non-linear curves of the elastic modulus,piezomagnetic coefficient,permeability,inductance and magneto-mechanical coupling factor of the magnetostrictive material with stress under different bias magnetic fields are calculated by using the Armstrong model.There are approximate quantities and trends of the curve,indicating that the Armstrong model can accurately describe the nonlinear characteristics of material parameters.(3)Based on the Young's modulus expression,Armstrong model,classical transfer matrix method and Bloch theorem,a nonlinear dynamic model of the magnetostrictive rod periodic structure with shunt circuit is established.The variation law of attenuation constant peak and the cut-off frequency of the Bragg band gap with stress under open circuit is analyzed.The optimal operating point of the device for vibration reduction is determined.The Bragg band gap,resonance band gap and resonance common band gap characteristics of the device under different shunt capacitance and stress are analyzed.The results show that smaller shunt capacitance,larger magneto-mechanical coupling factor and larger inductance can significantly improve the vibration reduction performance of the device.(4)Aiming at the problem of instability of the high-frequency displacement transmission curve in the bending vibration of the layered periodic structure with the classical transfer matrix method and based on the magnetostrictive linear constitutive equation,Euler Bernoulli beam theory and modal analysis method,the electromechanical two-way coupled dynamic model of the magnetostrictive layered periodic structure is established.Furthermore,displacement transmission curves of the layered structure under different shunt circuit are calculated and analyzed,indicating the model's calculation convergence and its vibration damping performance.This thesis plays an important role in the guiding the design,overall performance estimation,control and use of magnetostrictive periodic structures with shunt circuit.