Nonlinear Dynamics of a Flexible Multirod (Multibeam) System

Abstract

The paper presents a general nonlinear numerical model for the dynamic analysis of a spatial structure that includes chains of flexible rods, with rigid bodies between them, and different kinds of connections between all these components. Such a system is denoted a multirod or multibeam system. The model is derived using a multibody system approach. The motion of each rod includes elastic deformations that are superimposed on finite rigid body motions. The elastic model of each rod is nonlinear and includes bending in two perpendicular directions, torsion, axial motion, and warping. Any distribution of the rod properties can be considered. Finite elements are used to describe the deformations. Although the elastic derivation is confined to moderate deformations, any level of nonlinearity can be addressed by dividing each rod into sub-rods. The joints between the rods are general and may include springs and dampers. A new formulation of Lagrange method is used in order to derive the equations of motion. It offers various advantages concerning the accuracy, stability of the constraints, and the modeling of constraints. The model is validated by comparing its results with new experimental results. Good agreement is shown between the experimental and numerical results.