MDOF stochastic stability analysis and applications to a coupled rotating shaft system

Abstract

Stochastic stability analysis and generalization of moment Lyapunov exponents of multi-degree-of-freedom (MDOF) systems under white noise excitation were carried out using the transformation method and the perturbation method. Such systems represent coupled dynamic models exposed to stochastic disturbances and they are very common in engineering practice. The analysis of individual parts of a mechanical system does not give a clear picture of its real behavior as a whole, so the consideration of dynamic couplings is of great importance. This study proposes a generalized set of new transformations for MDOF systems that are necessary for obtaining Itô’s equations needed for further consideration of stochastic stability. The eigenvalue problem for moment Lyapunov exponents is derived and then solved by the method of perturbation. The generalized procedure is applied in an example of a rotating coupled shaft system whose dynamic behavior should be analyzed with at least four generalized coordinates. Similar models have so far been analyzed with limitations on SDOF and 2DOF systems that do not fully correspond to realistic models. The methodology demonstrated in the study could be applied more broadly, as it has the potential to analyze the dynamic stability of even more intricate or diverse systems whose dynamics have not been previously studied.