Formulation of Flexible Multibody Systems

Abstract

This paper deals with equations of motion of a flexible multibody system whose bodies are connected by rotational hinges. The equations of motion are derived by taking degrees of freedom of one body properly set in the system, hinge rotational angles, and modal coordinates of flexible bodies as independent variables. Kane's equations of motion are used in the derivation and each term in the equations is expressed in a convenient form for the efficient recursive calculation. The system with loop structure is also treated by cutting loops at proper hinges. Although arbitrary modes can be used to express the elastic motion of a flexible body, if the modes of the static deformation at hinges are used, the simulation accuracy is improved and the loop configuration is easily treated. An example of a simulation program based upon the formulation algorithm is also shown in the paper.