Port inversions of parametric Two-Input Two-Output Port models of flexible substructures

In the context of multi-body modeling techniques, this paper details the port inversion operations, which can be performed on the Two-Input-Two-Output Port (TITOP) model of a flexible substructure to take into account various boundary conditions and to assemble it with the other substructures of the whole system. From the model obtained considering the body is clamped at a parent point and free at some others child points, it is shown that the dynamics obtained under the free-free, free-clamped, clamped-clamped boundary conditions can be characterized analytically. The clamped-clamped condition and its link with the Craig-Bampton formulation are more particularly investigated, since it is required to model closed-kinematic chains of flexible bodies, like in truss structures, using a sub-structuring approach. Furthermore, the channel inversion operations are extended to the case of parameter varying models. The model of a triangular mechanism, fully parameterized according to the cross section parameters of each mechanism beams, is developed and validated. This model is used to illustrate the capabilities of this parametric approach to import the model in multi-domain simulation software and the possibility to optimize directly the mechanism design.