Reduced transfer matrix method for linear tree multibody systems

This paper introduces a linear version of the reduced multibody system transfer matrix method for studying the eigenvalue problems and steady-state responses of tree multibody systems. The core idea is to recursively transfer mechanical information between elements, utilizing a directed rooted tree to depict the system topology. Reduced transfer equations are provided for both spatial rigid and flexible bodies. For flexible bodies, the derivation is based on the dynamical equations from the finite element method and component mode synthesis. The effectiveness and numerical stability of this method is validated through three numerical examples.