Dynamics of spatial rigid–flexible multibody systems with uncertain interval parameters

A non-intrusive computation methodology is proposed to study the dynamics of rigid–flexible multibody systems with a large number of uncertain interval parameters. The rigid–flexible multibody system is meshed by using a unified mesh of the absolute nodal coordinate formulation (ANCF). That is, the flexible parts are meshed by using the finite elements of the ANCF, while the rigid parts are described via the ANCF reference nodes (ANCF-RNs). Firstly, the interval differential-algebraic equations are directly transformed into the nonlinear interval algebraic equations by using the generalized-alpha algorithm. Then, the Chebyshev sampling methods, including Chebyshev tensor product sampling method and Chebyshev collocation method, are used to transform the nonlinear interval algebraic equations into sets of nonlinear algebraic equations with deterministic sampling parameters. The proposed computation methodology is non-intrusive because the original generalized-alpha algorithm is not amended. OpenMP directives are also used to parallelize the solving process of these deterministic nonlinear algebraic equations. To circumvent the interval explosion problem and maintain computation efficiency, the scanning method is used to determine the upper and lower bounds of the deducted Chebyshev surrogate models. Finally, two numerical examples are studied to validate the proposed methodology. The first example is used to check the effectiveness of the proposed methodology. And the second one of a complex rigid–flexible robot with uncertain interval parameters shows the effectiveness of the proposed computation methodology in the dynamics analysis of complicated spatial rigid–flexible multibody systems with a large number of uncertain interval parameters.