Dynamic computation for rigid–flexible multibody systems with hybrid uncertainty of randomness and interval

© 2019, Springer Nature B.V. Considering the unavoidable uncertainty of material properties, geometry, and external loads existing in rigid–flexible multibody systems, a new hybrid uncertain computational method is proposed. Two evaluation indexes, namely interval mean and interval error bar, are presented to quantify the system response. The dynamic model of a rigid–flexible multibody system is built by using the absolute node coordinate formula (ANCF). The geometry size and external loads of rigid components are considered as interval variables, while the Young’s modulus and Poisson’s ratio of flexible components are expressed by a random field. The continuous random field is discretized to Gaussian random variables by using the expansion optimal linear estimation (EOLE) method. This paper proposes an orthogonal series expansion method, termed as improved Polynomial-Chaos-Chebyshev-Interval (PCCI) method, which solves the random and interval uncertainty under one integral framework. The improved PCCI method has some sampling points located on the bounds of interval variables, which lead to a higher accuracy in estimating the bounds of multibody systems’ response compared to the PCCI method. A rigid–flexible slider–crank mechanism is used as a numerical example, which demonstrates that the improved PCCI method has a higher accuracy than the PCCI method