Stochastic Dynamics Study Of Typical Shape Memory Alloy Systems

The research on dynamic mechanical properties of a new composite Shape Memory Alloy(SMA)has become one of the hot topics in the field of material mechanics engineering.Considering that random disturbances and nonlinear factors such as material characteristics and external environment may induce the complex dynamic behavior of the system,which seriously affects the safety and reliability of SMA material structures,it is of great guiding significance to accurately grasp the complex dynamics and its mechanism of SMA system for structural design,vibration reduction and engineering application.However,so far,most of the existing studies mainly consider the definite situation and only focus on numerical simulations,without theoretical analysis.Therefore,based on the constitutive relation of SMA material,this paper takes the typical SMA systems as the research object,establishes a dynamic model of SMA under random disturbance,and theoretically analyzes their dynamical behaviors by approximating analytical method.Then,the influence law of material parameters on the system dynamics is explored,and the vibration suppression and early warning problems are considered.The main works of this thesis are as follows:(1)The idealized Gaussian white noise usually cannot accurately describe the complex external environment,we explore dynamics of SMA spring oscillator system with a random narrow-band noise.The polynomial constitutive relation of SMA material is used to establish the stochastic SMA spring oscillator model.A multiple scale method is examined to achieve the theoretical analysis,and then the amplitude-frequency response relationship and steady-state moment of the system are obtained.The effects of external excitation amplitude,random excitation and ambient temperature on the mechanical properties of the system materials are discussed in detail.The results show that the obtained approximate analytical solutions are in good agreement with the numerical ones,which verifies the effectiveness of the theoretical method.The change of external excitation amplitude and ambient temperature will cause the system to produce multi-valued regions,which will changes the structure of the system solution,and the noise intensity of narrow-band random excitation can induce the random bifurcation of SMA spring oscillator.(2)Considering the influence of material characteristics,we further investigate active the nonlinear dynamic response of SMA spring oscillator with viscoelastic material property under random disturbance.A narrow-band noise and an exponential integral viscoelastic constitutive relationship are employed to model a new viscoelastic SMA model with random excitation.Subsequently,the established SMA model are theoretically analyzed through the classic Lindstedt-Poincaré method and multiple scale method,and the effects of noise intensity,viscoelastic parameters and viscoelastic coefficient on the mechanical properties of SMA system materials are discussed.The results indicate that the obtained approximate analytical solutions can fit the numerical ones well.When the amplitude or excitation frequency is in a specific range,low-amplitude oscillation and high-amplitude oscillation coexist,and the system appears bistable behavior at this time.In addition,the viscoelastic term can affect the nonlinear stiffness and structural damping of the system,and both viscoelastic parameters and noise intensity can induce random bifurcation of SMA spring oscillator system.(3)Based on the influence of damping material characteristics,we study the dynamic response and vibration suppression of SMA spring oscillator model with fractional viscoelastic characteristics under harmonic excitation.Compared with integer order,the fractional order can reflect the memory effect of viscoelastic materials more accurately.The viscoelastic characteristics of damping are described by fractional derivative,and the dynamic model of SMA spring oscillator with harmonic external excitation and fractional viscoelastic material characteristics is established.Then,the averaging method is examined to investigate the system theoretically.Its effectiveness is verified via numerical results,and influences of the system parameters are discussed in detail.Numerical results verify the effectiveness of the method,and the influence of system parameters are discussed in detail.In addition,the control problem of viscoelastic SMA system is studied by using fractional sliding mode control strategy.We find that the existence of fractional order will increase the vibration amplitude of the system,but it can be effectively suppressed the vibration under sliding mode control.(4)Considering that the noise intensity will lead to random bifurcation of the system,the early warning problem of the stability of viscoelastic SMA laminated beams excited by narrow-band noise is studied.Based on the viscoelastic SMA laminated beam model under random excitation,the system is theoretically analyzed by multiple scale method,and the influence of random disturbance on the mechanical properties of the system is discussed.According to the escape probability,we analyze the possibility of random bifurcation of the system under different noise intensities.The non-local concept high-risk area is defined,and the occurrence range of noise-induced system from low amplitude oscillation to high amplitude oscillation is predicted.It is found that the catastrophic high amplitude oscillation of SMA laminated beams induced by noise occurs before the bifurcation point of the deterministic model.The high-risk area quantifies the parameter range of the system material stability.The research results provide an effective early warning signal for SMA system,which can avoid the change of material stability.