A fresh look at the dynamics of a flexible body application to substructuring for flexible multibody dynamics

The general formulation of the dynamics of an elastic body undergoing arbitrary motion is revisited with emphasis on the orthogonality between rigid body motion and elastic deformation on the one hand, and on the appropriate definition of the relative velocities induced by elastic deformation on the other hand. A mixed displacement–velocity approach is adopted, thus allowing a local frame definition of velocities which results in simplification of the discretization and solution steps. The proposed formulation is applied to model reduction starting from a set of free-free elastic modes and attachment modes. The Herting–Martinez component mode synthesis method is used to replace the modal intensities by a body-frame nodal set of elastic degrees of freedom. A body-to-global frame transformation is then applied to the system equations in incremental form to avoid the use of Lagrange multipliers for expressing node-to-node connections. Examples are presented to assess the methodology proposed and its numerical implementation.