Rod-removal technique for flexible-rods in the framework of semi-recursive multibody formulation

Abstract

The slender rods experience mechanical deformation in most practical cases. The deformation should be modeled numerically since it affects the dynamics of the entire system. This paper models flexible slender-rods in a closed-loop multibody system by considering rods as variable-length constraint equations, and updating the positions and velocities. The principle behind this method is to use the rod-removal technique and the 3D semi-recursive multibody formulation. When applying the rod-removal technique, the rods-associated second-derivative-based inertial forces and velocity-dependent inertial forces and external forces must be calculated and assembled in the whole system. If consider the rod-flexibility, the stiffness equations of the removed flexible-rods, in turn, can be formulated based on beam finite elements. The finite element equations can be combined with the multibody equations of motion to perform the simulation of rigid–flexible multibody system. Two simple multibody systems with a flexible rod are employed to verify the effectiveness of the presented flexible-rod removal technique. A rigid–flexible vehicle model is taken as an example to investigate the effects of flexible-rods towards vehicle dynamics, where different initial velocities, sprung masses, and rod materials are considered. The numerical results describe how the dynamics of multibody systems changes when the deformation of flexible rods is considered. It proves that the effects of rod-flexibility must be taken into account for multibody systems especially in worse cases.