Nonlinear Dynamic Characteristics Of Magnetic Shape Memory Alloy Actuator

Magnetic shape memory alloy(MSMA)is a new type of smart material that can produce a shape memory effect under the magnetic field.Magnetic shape memory alloys have large strain characteristics similar to conventional shape memory alloys(SMA),as well as the rapid response characteristics of magnetostrictive materials,which makes MSMA a type of potential actuator material.MSMA actuator is a new type of smart material actuator.It has a much larger displacement than the piezoelectric actuator in the same size,and has a driving frequency much higher than that of ordinary shape memory alloy actuators.MSMA actuator has been one of the development directions of the medium-high frequency large displacement actuators.In this paper,the dynamic characteristics of MSMA actuators subjected to harmonic excitation and random excitation are studied,and the following results have been achieved:(1)A new nonlinear hysteresis model is proposed,where the derivative of strain respect to time is introduced to describe the loading and unloading processes.The shortcomings of traditional hysteresis models that use special functions and cause the difficulty for dynamic analysis are overcomed.The magnetic field intensity(MFI)-strain curves of MSMA materials in different compressive stresses and the stress-strain curves in different MFIs are measured through experiments;the nonlinear differential constitutive relationships describing the MSMA’s stress-strain curves and the MFI-strain curves are established respectively;the principal component analysis software SIMCA-P is used to obtain the MFI-stress-strain coupling relationship,and finally the accuracy of the established multi-field coupling constitutive model is verified by experimental data;(2)A two-degree-of-freedom nonlinear dynamic model of a simply supported beam with a MSMA driver under PD control is established for the first time,and the dynamic characteristics of the system are discussed.The new model overcomes the defects of the traditional model that only regards the MSMA driver as a source of vibration and ignores its own structure’s stiffness.A type of MSMA actuator is designed,and its dynamic model is established by Hamilton principle.The first-order approximate solution of the system is obtained by the multi-scale method,and the system’s stability is analyzed.The dynamic characteristics of the system are numerically simulated using MATLAB software,and several typical nonlinear dynamic characteristics such as equilibrium point,limit cycle,double period,multi-pulse orbit jumping,chaos,etc.are obtained.(3)A new method for the dynamic analysis of a strong nonliner system is proposed.The traditional hysteresis model is susceptible to the effect of loading rate.In the new method,the non-linear damping term are modified by the natural frequency ω,which eliminates the influence of the loading rate on the hysteretic loop.In order to solve the undetermined natural frequency ω,a kind of small parameter transformation is introduced to convert the large parameters ε into the small parameter α,an implicit function equation is solved to obtain the natural frequency of the strong nonlinear system.and the influences of the system’s parameters on the natural frequency are analyzed.It is found that the different nonlinear term have different influence on the natural frequency of the system.On this basis,the nonlinear dynamic characteristics of the MSMA actuator with cracks are also studied.The crack is expressed as the harmonic change of the stiffness with time,and the system’s dynamics model with time-varying stiffness is obtained.The stability of the steady-state solution of the system is analyzed using the multi-scale method.It is found that the system’s stable domain is affected by the time-varying stiffness parameter σ.When σ increases,the system’s stable domain is reduced;(4)The dynamic characteristics of a MSMA actuators under random disturbances is studied for the first time,and a bifurcation control idea that avoids large periodic vibrations caused by random disturbances by adjusting system parameters is proposed.The nonlinear dynamic model of a MSMA actuator under random disturbance is established,and the drift and diffusion coefficients of the system are solved.The maximum Lyapunov exponent of the system is obtained,and then the local stability and global stability of the system are analyzed.A new local stability analysis method is proposed,which can be applied to the stability analysis of any point in the state space.The steady-state probability density function of the system’s response is obtained,and the numerical simulation is carried out using Mathematics software to obtain the parameter conditions of stochastic bifurcation.Theoretical analysis and numerical simulation results show that there is stochastic Hopf bifurcation phenomenon in the hysteretic nonlinear system under random disturbance.The large periodic vibration caused by random disturbance occupies an important component in the output of the driver and directly affects the output accuracy of the driver.The stochastic Hopf bifurcation phenomenon can be controlled by adjusting the system parameters,the large periodic vibration caused by the random disturbance are avoid,and then the output accuracy of the MSMA driver is improved.