Stochastic semidiscretization method: Second moment stability analysis of linear stochastic periodic dynamical systems with delays

In this paper, an efficient numerical approach is presented, which allows the analysis of the moment dynamics, stability, and stationary behavior of linear periodic stochastic delay differential equations. The method leads to a high dimensional stochastic mapping with periodic statistical properties, from which the periodic first and second moment mappings are derived. The application of the method is demonstrated first through the analysis of the stochastic delay Mathieu equation. Then a practical case study, where the effect of spindle speed variation on the stability and the resulting surface quality of turning operations is investigated.