An explicit independent-coordinate formulation for the equations of motion of flexible multibody systems

In this paper, we develop an expression for the equations of motion of multibody systems with rigid and flexible bodies performing any kind of motion, with fixed and time-dependent holonomic constraints, forming open and closed loops, and with constant field forces and generic forces acting on the bodies. The proposed equations have been obtained by Lagrange’s approach and are formulated in terms of independent coordinates; influence coefficients, pseudo-velocities and pseudo-accelerations are used to take into account constraints; modal superposition techniques model body deformations; mass properties of flexible bodies are expressed by invariants of inertia. The final expression of the equations is suited for computer solution and is aimed at reducing to a minimum the number of kinematic analyses required to evaluate influence coefficients and their derivatives.