On the use of component mode synthesis methods for the model reduction of flexible multibody systems within the floating frame of reference formulation

Abstract

This paper is focused on the application of the fundamental model reduction techniques used in structural dynamics to flexible multibody systems. In particular, an effective computational approach is developed and tested in this work for adapting the conventional structural model condensation strategies to the dynamics of flexible multibody systems. Thereby, the synthesis methods considered in this work can be readily implemented in the principal computational framework used for modeling flexible multibody systems subjected to large reference displacements and small deformations, namely the Finite Element (FE) Floating Frame of Reference Formulation (FFRF). Three component mode synthesis methods are of interest for this study: the Guyan-Iron condensation method, the well-known modal truncation technique, and the Craig-Bampton synthesis approach. Employing the computational approach proposed in this paper, it is demonstrated by means of numerical experiments that the three fundamental reduction methods considered in this investigation lead to correct numerical results when used for obtaining condensed mechanical models of flexible multibody systems based on the FE-FFRF. In the case of flexible multibody systems, the computational approach developed in this paper consists of two fundamentally distinct steps. First, the reference conditions are formulated in the FE-FFRF in a way consistent with the geometric properties of the mechanical joints that connects the bodies of the flexible multibody system under consideration. This is a key step that allows the analyst to model multibody systems in complex geometric configurations. Subsequently, a reduction technique is selected and used for reducing the dimensionality of the problem at hand. It is remarked that the reference conditions assumed in the first step of the proposed computational procedure modify all the component modes resulting from the application of the reduction strategy chosen in the second step of the computational algorithm and may or may not delete some of these. In the second step of the computational approach mentioned before, the conventional model reduction techniques can be effectively used leading to consistent numerical results. In this work, three numerical examples are employed for demonstrating the effectiveness of the computational procedure developed in the paper. More importantly, considerations on the choice of either isostatic or hyperstatic reference conditions associated with a particular choice of component modes are discussed in detail throughout the manuscript. The numerical simulations demonstrate that these choices can have a significant influence also on the efficiency of the integration schemes.