Stochastic Component Mode Synthesis

Abstract

In this paper, a stochastic component mode synthesis method is developed for the dynamic analysis of large-scale structures with parameter uncertainties. The main idea is to represent each component displacement using a subspace spanned by a set of stochastic basis vectors in the same fashion as in stochastic reduced basis methods [1, 2]. These vectors represent however stochastic modes in contrast to the deterministic modes used in conventional substructuring methods [3]. The Craig-Bampton reduction procedure is used for illustration. A truncated set of stochastic fixed-free modes and a complete set of stochastic constraint modes are used to generate reduced matrices for each component. These are then coupled together through necessary compatibility constraints to form the global system matrices. The advantage of using stochastic component modes is that the Bubnov-Galerkin scheme can be applied for the computation of undetermined coefficients in the reduced approximation. Explicit expressions can be obtained for the responses in terms of the random parameters. Therefore the statistical moments of responses can be efficiently computed. The method is applied to a test case problem. Results obtained are compared with the traditional Craig-Bampton method, the first-order Taylor series and Monte Carlo Simulation benchmark results. We will refer to the proposed method as ROBUST or Reduced Order By Using Stochastic Techniques.