Dynamics of flexible multibody systems with hybrid uncertain parameters

The most popular way to study the dynamics of a multibody system with random parameters is the probabilistic method under the assumption that the mean values and variances of the random parameters are deterministic. For many engineering systems, however, the mean values and variances of those random parameters are inherently interval parameters. In this work, a new computation method is proposed to study the dynamics of flexible multibody systems with hybrid uncertain parameters, i.e., the random parameters with interval mean values and interval variances. The flexible multibody system of concern is described by using the Absolute Nodal Coordinate Formulation first. Then, the perturbation-based method is developed in order to incorporate hybrid uncertain parameters in the dynamic analysis of flexible multibody systems. Afterwards, the dynamics equations are expanded about the mean values of the uncertain input variables by means of the second-order Taylor series. The Chebyshev collocation method, together with the scanning method, is utilized to generate the interval bounds for the deduced surrogate model. Finally, the interval mean values and interval variances of the system dynamics are obtained by using the interval arithmetic. As a consequence, the proposed method can be degenerated into the pure interval method.