Automated Analysis of Constrained Systems of Rigid and Flexible Bodies

Abstract

This paper is concerned with modeling inertia properties of flexible components that undergo large angular rotations. Consistent, lumped and hybrid mass techniques are presented in detail and used to model the inertia properties of flexible bodies. The consistent formulation allows using the finite-element method as well as Rayleigh-Ritz method to describe the deformation of elastic components. Lumped mass techniques allow using shape vectors or experimentally identified data. In the hybrid mass formulation, the flexibility mass matrix is evaluated using a consistent mass formulation, while the inertia coupling between gross rigid body motion and elastic deformation is formulated using a lumped mass technique. Different mass formulations require the evaluation of similar sets of time-invariant matrices that represent the inertia coupling. Consequently, these matrices have to be evaluated only once in advance for the dynamic analysis. A unified mathematical model, and accordingly a unified computer program (DAMS: Dynamic Analysis of Multibody Systems), that deal with different formulations are developed. A comparative study is presented in order to study the effect of the mass formulation on the dynamic response of elastodynamic constrained systems. The validity of the linear theory that neglects the effect of small oscillations on large rigid body motion is also discussed.