Study On Nonlinear Dynamic Characteristics Of Magnetic Shape Memory Alloys Smart Structures

Magnetic shape memory alloy(MSMA)has the large deformation characteristics of shape memory alloy and the high response speed of giant magnetostrictive materials.It also has advantages of high energy density and good controllability.It is regarded as the preferred material to micro actuator and controller.In this paper,the nonlinear differential terms are introduced to establish the hysteretic nonlinear constitutive model of MSMA using hysteretic nonlinear theory based on the experimental data of magnetic shape memory alloy materials.Considering the influence of the compressive stress on the magnetic field intensity(MFI)-strain hysteretic curves,the principal component analysis method of the modern multivariate statistical regression theory has been applied to obtain the nonlinear coupling relationships among strain,magnetic field intensity and compressive stress.Similarly,the relationships among strain,stress and MFI of MSMA have also been discussed.On this basis,the nonlinear dynamic model of magnetic shape memory alloy structure is established in Hamilton's principle and nonlinear elastic mechanics theory.The dynamic equations of a simply-supported beam,simply-supported plate,and actuator are established.The approximate solution and the stability of the system are obtained by the multi-scale method.MATLAB software is applied in numerical simulation of the system.The different time-velocity,time-displacement and phase diagrams of the system are obtained by adjusting the parameters of the system,and several meaningful results such as equilibrium point,limit cycle,multi-period and chaos are analyzed.Based on the above,the nonlinear stochastic dynamic model of the system is set up where the influence of random disturbance on the system is considered.The local stability and global stability of system are analyzed,and the stochastic responses of the system are obtained.Finally,the stochastic bifurcation characteristics of the system are discussed.The results of this paper have important theoretical significance and engineering application value to promote the research and application of magnetic shape memory alloy materials in engineering.