Keywords: stochastic averaging method, maximal Lyapunov exponent, singular boundary, stochastic P-bifurcation and D-bifurcation.

Considering the Gauss white noise stochastic parametric excitation, a stochastic dynamic model of a suspended wheelset is established. According to the Hamilton system and the stochastic differential equation theory, the model can be expressed as a quasi-non-integrable Hamiltonian system in the form of the Ito stochastic differential equation. The equation can be reduced to one dimensional diffusion Ito average stochastic differential equation using the stochastic averaging method. Therefore the solution of the original system converges in probability to the one dimensional Ito diffusion process.

First, the maximal Lyapunov exponent was calculated using Oseledec multiplicative ergodic theory, the local stochastic stability condition is obtained when the maximal Lyapunov exponent is less than 0. Then, the global stochastic stability was researched by judging the modality of the singular boundary. The diffusion exponent, drift exponent and character value of the left boundary and the right boundary were calculated. Finally, the stationary probability density of the system response was calculated. By analyzing the shape and peaks of the stationary probability density function, the conditions of stochastic P-bifurcation and D-bifurcation were obtained.

The results show that the stochastic excitation plays an important role in the system, the stochastic system becomes more sensitive and more unstable, and the random excitation drift forward the critical speed exhibited in the deterministic system. Therefore, the stochastic excitation cannot be ignored when considering the stability of vehicle system, and the safety margin must be sufficient in the vehicle design.

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