Multiple dynamic response patterns of flexible multibody systems with random uncertain parameters
Zhe Wang, Qiang Tian and Haiyan Hu
Abstract: The mechanisms with uncertain parameters may exhibit multiple dynamic response patterns. As a single surrogate model can hardly describe all the dynamic response patterns f mechanism dynamics, a new computation methodology is proposed to study multiple dynamic response patterns of a flexible multibody system with uncertain random parameters. The flexible multibody system of concern is modeled by using a unified mesh of the absolute nodal coordinate formulation (ANCF). The polynomial chaos (PC) expansion with collocation methods is used to generate the surrogate model for the flexible multibody system with random parameters. Several sub-surrogate models are used to describe multiple dynamic response patterns of the system dynamics. By the motivation of the data mining, the Dirichlet process mixture model (DPMM) is used to determine the dynamic response patterns and project the collocation points into different patterns. The uncertain differential algebraic equations (DAEs) for the flexible multibody system are directly transformed into the uncertain nonlinear algebraic equations by using the generalized-alpha algorithm. Then, the PC expansion is further used to transform the uncertain nonlinear algebraic equations into several sets of nonlinear algebraic equations with deterministic collocation points. Finally, two numerical examples are presented to validate the proposed methodology. The first confirms the effectiveness of the proposed methodology, and the second one shows the effectiveness of the proposed computation methodology in multiple dynamic response patterns study of a complicated spatial flexible multibody system with uncertain random parameters.
