A Motion Formalism Approach to Modal Reduction for Flexible Multibody System Applications

Multibody systems are often modeled as interconnected multibody and modal components: multibody components, such as rigid bodies, beams, plates, and kinematic joints, are treated via multibody techniques whereas the modal components are handled via a modal reduction approach based on the small strain assumption. In this work, the problem is formulated within the framework of the motion formalism. The kinematic description involves simple, straightforward frame transformations and leads naturally to consistent deformation measures. Derivatives are expressed in local frames, which results in the remarkable property that the tangent matrices are independent of the position and orientation of the modal component with respect to an inertia frame. This implies a reduced level of geometric non-linearity as compared to standard description. In particular, geometrically non-linear problems can be solved with the tangent matrices of the reference configuration, without re-evaluation and re-factorization.