ELASTODYNAMICS OF MULTIBODY SYSTEMS USING GENERALIZED INERTIAL COORDINATES AND STRUCTURAL DAMPING

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 a pplied 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 matri x must be derived for each particular type of finite element used in t he description of the flexible body. Applying a lumped mass formulatio n and referring nodal displacements to the inertial frame, rather than to the body-fixed coordinate frame, yields a constant diagonal mass m atrix for a flexible body. Coupling between the large rigid body motio n and the small elastic deformations is still preserved. Kinematic con straints are introduced in the multibody system equations, using the n ew coordinates. Efficiencies and limitations of the proposed formulati on are discussed, based on the simulation of several models of a simpl e planar multibody system with increasing complexity and various dampi ng ratios.