Stability and Bifurcation in Multi-Scaled Stochastic Mechanics

Abstract

This paper investigates simulation schemes of high order and correspondingly extended covariance equations. Both are derived by multiply iterated integrals and applied to road-vehicle systems. To avoid numerical instabilities for infinitely growing vehicle speed, inverse scales are introduced into the time domain. In case of cubic-progressive wheel suspensions, it can be shown that the stationary rms-values (root-mean-square) of the vehicle vibrations bifurcate into periodical ones even when the vehicle damping is strictly positive but weak.