Reduced-order modeling of Hamiltonian formulation in flexible multibody dynamics: Theory and simulations

Abstract

Flexible multibody dynamics has been developed as an effective method for analyzing mechanical structures, wherein the Hamiltonian formulation draws attention for advantages such as the systematic handling of systems with varying mass. However, the utilization of the finite element method typically results in a large number of variables, which deteriorates computational efficiency. An effective method to reduce the number of variables (coordinates and canonical conjugate momentum) in Hamiltonian formulation needs to be presented. This paper proposes a novel reduced-order modeling of the Hamiltonian formulation based on the component mode synthesis method. A novel definition of momentum is proposed to construct the equation of motion. Compared with conventional Hamiltonian formulations, not only generalized coordinates but also momentum is reduced. By combining the absolute nodal coordinate formulation with the proposed formulation, it is applicable to analyze nonlinear structures with large deformation and rotations. Four numerical simulations were conducted to evaluate the performance of the proposed formulation, and calculation time reductions of 52.1 %, 83.6 %, 93.4 %, and 81.5 % were achieved. Overall, the proposed Hamiltonian formulation exhibits high calculation efficiency, good numerical stability, and high accuracy.