Further investigation on the coupling between the reference and elastic displacements in flexible body dynamics

A new semi-analytical multibody system (MBS) model derived using general nonlinear flexible body dynamics formulation is developed in this investigation. The semi-analytical model can serve as a benchmark example for testing the implementation of the finite element (FE) floating frame of reference (FFR) formulation in commercial MBS software. In particular, this new model sheds light on the important concept of the reference conditions which is fundamental in the computer implementation of the FE/FFR formulation. In order to develop the new FE/FFR semi-analytical model, the reference motion of the flexible body is expressed in terms of specified motion trajectories, allowing for developing a set of second-order ordinary differential equations (ODE's) with time-varying coefficients. The FE/FFR inertia shape integrals are evaluated and used to define the generalized forces associated with the deformation coordinates. The simplifications that result from the use of the mean-axis reference conditions are highlighted and the significance of these simplifications on the solution accuracy when using more appropriate sets of reference conditions is discussed. It is shown that if a MBS computer algorithm restricts the choice of the reference conditions to one set, the use of other reference conditions can lead to a homogeneous ODE system with time-varying coefficients which has zero solution in the case of zero initial conditions and zero external forces regardless of the flexible body reference rotation.