Elastodynamics of Multibody Systems Using Generalized Inertial Coordinates and Structural Damping*

Abstract

ABSTRACT A new formulation to describe the elastodynamics of flexible multibody systems using efficient generalized inertial coordinates is presented and discussed in this paper. The finite element method is initially applied to the continuum mechanics equations of the system components, leading to equations of motion for flexible bodies in which the linear elastodynamics is effectively coupled with the body gross motion by a time variant mass matrix. However, the coefficients of the mass matrix must be derived for each panicular type of finite element used in the description of the flexible body. Applying a lumped mass formulation and referring nodal displacements to the inertial frame, rather than to the body-fixed coordinate frame, yields a constant diagonal mass matrix for a flexible body. Coupling between the large rigid body motion and the small elastic deformations is still preserved. Kinematic constraints are introduced in the multibody system equations, using the new coordinates. Efficiencies and limitations of the proposed formulation are discussed, based on the simulation of several models of a simple planar multibody system with increasing complexity and various damping ratios.