Global flexible modes for the model reduction of planar mechanisms using the finite-element floating frame of reference formulation

In this paper, a novel reduction method for planar flexible mechanisms based on global flexible modes is proposed. Using the framework provided by the finite-element floating frame of reference formulation (FE-FFRF), the global flexible modes of a planar mechanism are derived from the linearized modal equations of motion at a given linearization point. The global flexible modes are consistent with the reference conditions necessary to prevent rigid body motions of the finite elements inside their floating frames of reference. Furthermore, the global flexible modes satisfy the multibody joints constraints of the mechanism. These features make the global flexible modes eligible to be used as local normal modes for the reduction of single components. In this first use, referred to as the GNMC, the global modes are employed to substitute the normal modes obtained using the conventional normal mode approach. In the second use, referred to as the GNMS, the global flexible modes impose global shapes to the whole mechanism allowing for a global reduction of the flexible coordinates. Two benchmark problems are reported to show the feasible applications of the proposed method. The numerical results of the global method are compared to those coming from the models without reduction and from the models reduced through the normal mode approach and the Craig-Bampton method.