Jac. Ambrosio et P. Ravn, ELASTODYNAMICS OF MULTIBODY SYSTEMS USING GENERALIZED INERTIAL COORDINATES AND STRUCTURAL DAMPING, Mechanics of structures and machines, 25(2), 1997, pp. 201-219
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.