Time-variant response computation of flexible multibody systems with imprecise random fields

This paper proposes a new uncertain modelling and analysis method for flexible multibody systems with imprecise random field uncertainties. The standard random field is expanded to the imprecise random field model containing the behavior of imprecise randomness with bounded statistical moments more appropriately for real engineering problems. The imprecise random field is further discretized to independent standard Gaussian random variables by using the Karhunen-Loève expansion method. The flexible multibody system is modeled by using a unified mesh of the absolute node coordinate formula. Mathematical expressions and solution procedure based on the Polynomial chaos-Legendre metamodel are developed to solve the dynamic equations of systems involving imprecise random field. Two types of evaluation indexes are effectively established by constructing the second layer polynomial chaos expansion, namely interval mean value, interval variance, mean of the upper bound, variance of the lower bound. Finally, the effectiveness of the presented method is illustrated by two numerical examples of flexible multibody systems. Especially, for complicated multibody systems, it is necessary to calculate two uncertainty evaluation indexes to study the complete dynamic behavior.