The Research Of Stochastic Nonlinear Dynamics On The Intelligent Semi-active Suspension System

Vehicle semi-active suspension system is the main compenent in cars to ride safety and to drive comfortable. The research of vehicle semi-active suspension system has become a current focus, but there is less research on the intelligent vehicle semi-active suspension system whose stiffness of elastic elements could be controlled, and there is even less research with the stochastic nonlinear dynamics theory. In this paper, we research on the stochastic dynamics characteristics of vehicle semi-active suspension system with Magnetically Controlled Shape Memory Alloy (MSM) spring actuator, The main content is as follows:A vehicle semi-active suspension system with MSMA spring actuator is built, considering the impact of uneven tire materials and other internal random factors. Simplifying the model with stochastic average method, the max Lyapunov exponent of the model is calculated by quasi non-integrable Hamiltonian theory and Oseledec multiplicative ergodic theory, the local stability conditions has been obtained; the global stability of vehicle semi-active suspension stochastic system is decided using the boundary behavior of stochastic system, and the global stability conditions has been obtained. By calculating the max Lyapunov exponent of stochastic system and solving the FPK equation of the stable probability density function, the condition of stochastic Hopf bifurcation of the suspension vibration model has been obtained, and do the numerical simulation of the stable probability density function in order to verify the results of the theoretical analysis.By judging the modality of the singular boundary of vehicle semi-active suspension stochastic vibration system, the condition of the first-passage behavior is calculated, and the backward Kolmogorov equation for reliability function and probability density function of the first-passage time is established. On the basis, combined with the initial conditions and boundary conditions, the first-passage issue is derived, the numerical simulation which respectively takes initial energy, noise intensity, equivalent stiffness of tire and the controllable parameters of MSMA spring actuator as variable has been done. The model of the controlled suspension system has been established by adding the control unit, the optimal control strategy aimed to obtain the maximization of reliable function had been accessed by dynamic programming principles. Numerical simulation of partial differential equations fitted for reliability function and probability density function of the first-passage time has been obtained by finite difference methods. In the Numerical simulation, we respectively take controlled binding force, initial energy, noise intensity, equivalent stiffness of tire and the controllable parameters of MSMA spring actuator as variable...